Question 1

Choose the one alternative that best completes the statement or answers the question.
-How many ways can two Republicans, one Democrat, and one Independent be chosen from nine Republicans,
five Democrats, and two Independents to fill four positions on city council?

Accepted Answer

The answer of  Choose the one alternative that best...

Question 2

Choose the one alternative that best completes the statement or answers the question.
-How many ways can five people, A, B, C, D, and E, sit in a row at a movie theater if D and E will not sit next to each other?
A)72
B)24
C)48
D)60

Accepted Answer

The answer of  Choose the one alternative that best...

Question 3

Choose the one alternative that best completes the statement or answers the question.
-How many different permutations of the letters in the word PROBABILITY are there?

Accepted Answer

The answer of  Choose the one alternative that best...

Question 4

Choose the one alternative that best completes the statement or answers the question.
-How many ways can a jury of four men and three women be selected from twelve men and ten women?

Accepted Answer

The answer of  Choose the one alternative that best...

Question 5

Choose the one alternative that best completes the statement or answers the question.
-If a couple plans to have eleven children, how many gender sequences are possible?
A)2048
B)11
C)2.853116706e+11
D)121

Accepted Answer

For each child, there are two possible genders (male or female). Therefore, for eleven children, there are 2^11 possible gender sequences, which is equal to 2048.

Question 6

Choose the one alternative that best completes the statement or answers the question.
-The access code to a houseʹs security system consists of five digits. How many different codes are available if
the first digit cannot be zero and the arrangement of five fives is excluded?

Accepted Answer

The answer of  Choose the one alternative that best...

Question 7

Choose the one alternative that best completes the statement or answers the question.
-How many versions of a test are required to cover all possible question arrangements if there are seven
open-ended questions on the test?

Accepted Answer

The answer of  Choose the one alternative that best...

Question 8

Decide if the situation involves permutations, combinations, or neither. Explain your reasoning.
-The number of five-letter passwords that can be created when letters can be repeated

Accepted Answer

The answer of Decide if the situation involves permutations, combinations,...

Question 9

Choose the one alternative that best completes the statement or answers the question.
-A delivery route must include stops at eight cities. How many different routes are possible?
A)40,320
B)8
C)256
D)16,777,216

Accepted Answer

The number of different routes possible is calculated by finding the factorial of the number of cities, which is 8! = 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1 = 40,320.

Question 10

Choose the one alternative that best completes the statement or answers the question.
-Eight guests are invited for dinner. How many ways can they be seated at a dinner table if the table is straight with seats only on one side?
A)40,320
B)362,880
C)5040
D)1

Accepted Answer

The number of ways to arrange 8 guests in a straight line is 8 factorial (8!), which equals 40,320.

Question 11

Choose the one alternative that best completes the statement or answers the question.
-How many ways can five people, A, B, C, D, and E, sit in a row at a movie theater if A and B must sit together?
A)48
B)120
C)12
D)24

Accepted Answer

If A and B must sit together, treat them as a single unit or "block." This means we have four units to arrange: (AB), C, D, and E. The number of ways to arrange these four units is 4! = 24. Within the block, A and B can switch places, giving us 2! = 2 ways. Therefore, the total number of arrangements is 24 * 2 = 48.

Question 12

Choose the one alternative that best completes the statement or answers the question.
-In California, each automobile license plate consists of a single digit followed by three letters, followed by three
digits. How many distinct license plates can be formed if there are no restrictions on the digits or letters?

Accepted Answer

The answer of  Choose the one alternative that best...

Question 13

Choose the one alternative that best completes the statement or answers the question.
-How many ways can five people, A, B, C, D, and E, sit in a row at a movie theater if C must sit to the right of but not necessarily next to B?
A)60
B)24
C)20
D)48

Accepted Answer

There are 5! = 120 total ways to arrange five people. Half of these arrangements will have C to the right of B, so 120/2 = 60 ways.

Question 14

Choose the one alternative that best completes the statement or answers the question.
-The Environmental Protection Agency must visit nine factories for complaints of air pollution. In how many different ways can a representative visit five of these to investigate this week?
A)15,120
B)362,880
C)5
D)126

Accepted Answer

The number of ways to choose 5 factories out of 9 is given by the combination formula:C(9, 5) = 9! / (5! * 4!) = 15,120

Question 15

Decide if the situation involves permutations, combinations, or neither. Explain your reasoning.
-The number of ways an airline can hire a flight attendant for its European flights, a flight attendant for its
domestic flights, and a flight attendant for its Asian flight from a pool of 35 applicants

Accepted Answer

The answer of Decide if the situation involves permutations, combinations,...

Question 16

Choose the one alternative that best completes the statement or answers the question.
-The access code to a houseʹs security system consists of six digits. How many different codes are available if each digit can be repeated?
A)1,000,000
B)46,656
C)64
D)6

Accepted Answer

There are 10 possible choices for each of the six digits (0-9), so the total number of possible codes is 10^6 = 1,000,000. There are 10 possible digits (0-9) for each of the 6 positions in the access code. Therefore, the total number of possible codes is: 
10 x 10 x 10 x 10 x 10 x 10 = 1,000,000. So, the correct answer is A.

Question 17

Choose the one alternative that best completes the statement or answers the question.
-A tourist in Ireland wants to visit six different cities. How many different routes are possible?
A)720
B)120
C)36
D)46,656

Accepted Answer

The number of different routes possible is calculated by finding the factorial of the number of cities, which is 6 factorial (6!) = 720.

Question 18

Choose the one alternative that best completes the statement or answers the question.
-How many different permutations of the letters in the word STATISTICS are there?

Accepted Answer

The answer of  Choose the one alternative that best...

Question 19

Choose the one alternative that best completes the statement or answers the question.
-If a couple has six boys and six girls, how many gender sequences are possible?
A)924
B)12
C)8
D)16

Accepted Answer

There are 12 children, so the number of gender sequences can be calculated using the formula for permutations: P(12,12) = 12!/(12-12)! = 12! = 479001600. However, since we only need to consider the gender sequences, we need to divide by the number of ways the boys and girls can be ordered within their own groups, which is given by 6! and 6!, respectively. Therefore, the total number of possible gender sequences is 12!/(6!6!) = 924. The number of gender sequences can be found by calculating the number of ways to arrange 12 items (6 boys and 6 girls) in a row, which is 12!. However, we must divide by the number of ways to arrange the identical items, which is 6! for the boys and 6! for the girls. Therefore, the total number of gender sequences is 12!/6!6! = 924.

Question 20

Choose the one alternative that best completes the statement or answers the question.
-A student must answer seven questions on an exam that contains twelve questions.
a)How many ways can the student do this?
b)How many ways are there if the student must answer the first and last question?

Accepted Answer

The answer of  Choose the one alternative that best...

Quiz 3: Probability

Choose the one alternative that best completes the statement or answers the question. -How many ways can two Republicans, one Democrat, and one Independent be chosen from nine Republicans, five Democrats, and two Independents to fill four positions on city council?

Choose the one alternative that best completes the statement or answers the question. -How many ways can five people, A, B, C, D, and E, sit in a row at a movie theater if D and E will not sit next to each other?

Choose the one alternative that best completes the statement or answers the question. -How many different permutations of the letters in the word PROBABILITY are there?

Choose the one alternative that best completes the statement or answers the question. -How many ways can a jury of four men and three women be selected from twelve men and ten women?

Choose the one alternative that best completes the statement or answers the question. -If a couple plans to have eleven children, how many gender sequences are possible?

Choose the one alternative that best completes the statement or answers the question. -The access code to a houseʹs security system consists of five digits. How many different codes are available if the first digit cannot be zero and the arrangement of five fives is excluded?

Choose the one alternative that best completes the statement or answers the question. -How many versions of a test are required to cover all possible question arrangements if there are seven open-ended questions on the test?

Decide if the situation involves permutations, combinations, or neither. Explain your reasoning. -The number of five-letter passwords that can be created when letters can be repeated

Choose the one alternative that best completes the statement or answers the question. -A delivery route must include stops at eight cities. How many different routes are possible?

Choose the one alternative that best completes the statement or answers the question. -Eight guests are invited for dinner. How many ways can they be seated at a dinner table if the table is straight with seats only on one side?

Choose the one alternative that best completes the statement or answers the question. -How many ways can five people, A, B, C, D, and E, sit in a row at a movie theater if A and B must sit together?

Choose the one alternative that best completes the statement or answers the question. -How many ways can five people, A, B, C, D, and E, sit in a row at a movie theater if C must sit to the right of but not necessarily next to B?

Choose the one alternative that best completes the statement or answers the question. -The Environmental Protection Agency must visit nine factories for complaints of air pollution. In how many different ways can a representative visit five of these to investigate this week?

Decide if the situation involves permutations, combinations, or neither. Explain your reasoning. -The number of ways an airline can hire a flight attendant for its European flights, a flight attendant for its domestic flights, and a flight attendant for its Asian flight from a pool of 35 applicants

Choose the one alternative that best completes the statement or answers the question. -The access code to a houseʹs security system consists of six digits. How many different codes are available if each digit can be repeated?

Choose the one alternative that best completes the statement or answers the question. -A tourist in Ireland wants to visit six different cities. How many different routes are possible?

Choose the one alternative that best completes the statement or answers the question. -How many different permutations of the letters in the word STATISTICS are there?

Choose the one alternative that best completes the statement or answers the question. -If a couple has six boys and six girls, how many gender sequences are possible?

Choose the one alternative that best completes the statement or answers the question. -A student must answer seven questions on an exam that contains twelve questions. a)How many ways can the student do this? b)How many ways are there if the student must answer the first and last question?