Question 1

A consumer testing service is commissioned to rank the top 4 brands of dishwasher detergent. Ten brands are to be included in the study. In how many different ways can the consumer testing service arrive at the ranking?

Accepted Answer

The answer of A consumer testing service is commissioned to...

Question 2

A panel of coaches ranks the high school football teams in a particular state each week. The panel unanimously agrees on which five teams should comprise the top five but not on the order. In how many different ways can the coaches rank the top five teams?

Accepted Answer

The answer of A panel of coaches ranks the high...

Question 3

Find the numerical value of $$P _ { 4 } ^ { 6 }$$ .

Accepted Answer

The answer of Find the numerical value of \[P _...

Question 4

Suppose there are four dangerous military missions, each requiring one soldier. In how many different ways can 4 soldiers from a squadron of 100 be assigned to these four missions?

Accepted Answer

The answer of Suppose there are four dangerous military missions,...

Question 5

$$\mathrm { P } _ { 4 } ^ { 10 }$$

Accepted Answer

The answer of \[\mathrm { P } _ { 4...

Question 6

$\left( \begin{array} { l } 
90 \
90
\end{array} \right)$

Accepted Answer

The binomial coefficient $\left( \begin{array} { c } n \k\end{array} \right)$ is equal to 1 when $n = k$. Here, $n = 90$ and $k = 90$, so the value is 1.

Question 7

$\left( \begin{array} { c } 
70 \
0
\end{array} \right)$

Accepted Answer

The binomial coefficient $\left( \begin{array} { c } 70 \ 0 \end{array} \right)$ is equal to 1, as choosing 0 items from 70 is always 1 way.

Question 8

$$\mathrm { P } _ { 4 } ^ { 8 }$$

Accepted Answer

The answer of \[\mathrm { P } _ { 4...

Question 9

You have 5 tasks to complete and 15 people, including yourself, to complete the tasks. In how many ways can you assign 3 people to each task?

Accepted Answer

The answer of You have 5 tasks to complete and...

Question 10

You have 4 tasks to complete and 10 people, including yourself, to complete the tasks. In how many ways can you assign 4 people to the first task, 3 people to the second task, 2 people to the third task, and 1 person to the fourth task?

Accepted Answer

The answer of You have 4 tasks to complete and...

Question 11

There are 15 candidates for three different executive positions. How many different ways could you fill the positions?

Accepted Answer

The answer of There are 15 candidates for three different...

Question 12

A manager of a road construction company must send one engineer to each of three different job sites to meet with government inspectors. There are 8 engineers available. How many different ways can the manager send one engineer to each of the job sites? (Assume that sending a particular engineer to job site 1 is different than sending the same engineer to either job site 2 or 3.)

Accepted Answer

The manager can choose an engineer for the first job site in 8 ways, for the second job site in 7 ways (since one engineer is already assigned), and for the third job site in 6 ways. Therefore, the total number of ways is 8 * 7 * 6 = 336.

Question 13

Find the numerical value of $$P \frac { 5 } { 5 }$$ .

Accepted Answer

P is a prime number and 5 is a prime number. So, $$P \frac { 5 } { 5 } = P^5$$. P is a prime number, so $$P^5$$ is a prime number. The only prime number that is a perfect square is 2. So, $$P = 2$$. Therefore, $$P \frac { 5 } { 5 } = 2^5 = 32$$.

Question 14

Which expression is equivalent to $P _ { n } ^ { N }$ ?
A) $\frac { N ! } { ( N - n ) ! }$

B) $\frac { N ! } { n ! }$

C) $\frac { N ! } { n ! ( N - n ) ! }$

D) $\frac { N ! n ! } { ( N - n ) ! }$

Accepted Answer

The answer of Which expression is equivalent to \(P _...

Question 15

$\left( \begin{array} { l } 
70 \
68
\end{array} \right)$

Accepted Answer

The answer of \(\left( \begin{array} { l } 
70 \
68
\end{array}...

Question 16

Suppose you teach a class of twelve students that you wish to assign to three groups of four students each. In how many different ways can groups be made?

Accepted Answer

The number of ways to divide 12 students into 3 groups of 4 is calculated using the formula for combinations of dividing n items into groups of equal size: (12!)/(4!4!4!3!) = 34,650.

Question 17

A group of 12 people is traveling in three vehicles. If 4 people ride in each vehicle, in how many different ways can the people be assigned to the vehicles?

Accepted Answer

There are 12 people and 3 vehicles. So, the number of ways to assign people to vehicles is 12P3 = 11,880.

Question 18

$$\mathrm { P } _ { 0 } ^ { 12 }$$

Accepted Answer

The notation $\mathrm{P}_0^{12}$ represents the number of permutations of 12 items taken 0 at a time, which is always 1.

Question 19

A group of 13 people is traveling in three vehicles. If 6 people ride in the van, 5 people ride in the car, and 2 people ride in the pickup, in how many different ways can the people be assigned to the vehicles?

Accepted Answer

The answer of A group of 13 people is traveling...

Question 20

$\left( \begin{array} { l } 
9 \
4
\end{array} \right)$

Accepted Answer

The answer of \(\left( \begin{array} { l } 
9 \
4
\end{array}...

Quiz 3: Probability

A consumer testing service is commissioned to rank the top 4 brands of dishwasher detergent. Ten brands are to be included in the study. In how many different ways can the consumer testing service arrive at the ranking?

A panel of coaches ranks the high school football teams in a particular state each week. The panel unanimously agrees on which five teams should comprise the top five but not on the order. In how many different ways can the coaches rank the top five teams?

Find the numerical value of $P _ { 4 } ^ { 6 }$ .

Suppose there are four dangerous military missions, each requiring one soldier. In how many different ways can 4 soldiers from a squadron of 100 be assigned to these four missions?

$\mathrm { P } _ { 4 } ^ { 10 }$

$\left( \begin{array} { l } 90 \\90\end{array} \right)$

$\left( \begin{array} { c } 70 \\0\end{array} \right)$

$\mathrm { P } _ { 4 } ^ { 8 }$

You have 5 tasks to complete and 15 people, including yourself, to complete the tasks. In how many ways can you assign 3 people to each task?

You have 4 tasks to complete and 10 people, including yourself, to complete the tasks. In how many ways can you assign 4 people to the first task, 3 people to the second task, 2 people to the third task, and 1 person to the fourth task?

There are 15 candidates for three different executive positions. How many different ways could you fill the positions?

Find the numerical value of $P \frac { 5 } { 5 }$ .

Which expression is equivalent to $P _ { n } ^ { N }$ ? A) $\frac { N ! } { ( N - n ) ! }$ B) $\frac { N ! } { n ! }$ C) $\frac { N ! } { n ! ( N - n ) ! }$ D) $\frac { N ! n ! } { ( N - n ) ! }$

$\left( \begin{array} { l } 70 \\68\end{array} \right)$

Suppose you teach a class of twelve students that you wish to assign to three groups of four students each. In how many different ways can groups be made?

A group of 12 people is traveling in three vehicles. If 4 people ride in each vehicle, in how many different ways can the people be assigned to the vehicles?

$\mathrm { P } _ { 0 } ^ { 12 }$

A group of 13 people is traveling in three vehicles. If 6 people ride in the van, 5 people ride in the car, and 2 people ride in the pickup, in how many different ways can the people be assigned to the vehicles?

$\left( \begin{array} { l } 9 \\4\end{array} \right)$

Quiz 3: Probability

A consumer testing service is commissioned to rank the top 4 brands of dishwasher detergent. Ten brands are to be included in the study. In how many different ways can the consumer testing service arrive at the ranking?

A panel of coaches ranks the high school football teams in a particular state each week. The panel unanimously agrees on which five teams should comprise the top five but not on the order. In how many different ways can the coaches rank the top five teams?

Find the numerical value of P46P _ { 4 } ^ { 6 }P46​ .

Suppose there are four dangerous military missions, each requiring one soldier. In how many different ways can 4 soldiers from a squadron of 100 be assigned to these four missions?

P410\mathrm { P } _ { 4 } ^ { 10 }P410​

(9090) \left( \begin{array} { l } 90 \\90\end{array} \right) (9090​)

(700) \left( \begin{array} { c } 70 \\0\end{array} \right) (700​)

P48\mathrm { P } _ { 4 } ^ { 8 }P48​

You have 5 tasks to complete and 15 people, including yourself, to complete the tasks. In how many ways can you assign 3 people to each task?

You have 4 tasks to complete and 10 people, including yourself, to complete the tasks. In how many ways can you assign 4 people to the first task, 3 people to the second task, 2 people to the third task, and 1 person to the fourth task?

There are 15 candidates for three different executive positions. How many different ways could you fill the positions?

Find the numerical value of P55P \frac { 5 } { 5 }P55​ .

Which expression is equivalent to PnNP _ { n } ^ { N }PnN​ ? A) N!(N−n)!\frac { N ! } { ( N - n ) ! }(N−n)!N!​ B) N!n!\frac { N ! } { n ! }n!N!​ C) N!n!(N−n)!\frac { N ! } { n ! ( N - n ) ! }n!(N−n)!N!​ D) N!n!(N−n)!\frac { N ! n ! } { ( N - n ) ! }(N−n)!N!n!​

(7068) \left( \begin{array} { l } 70 \\68\end{array} \right) (7068​)

Suppose you teach a class of twelve students that you wish to assign to three groups of four students each. In how many different ways can groups be made?

A group of 12 people is traveling in three vehicles. If 4 people ride in each vehicle, in how many different ways can the people be assigned to the vehicles?

P012\mathrm { P } _ { 0 } ^ { 12 }P012​

A group of 13 people is traveling in three vehicles. If 6 people ride in the van, 5 people ride in the car, and 2 people ride in the pickup, in how many different ways can the people be assigned to the vehicles?

(94) \left( \begin{array} { l } 9 \\4\end{array} \right) (94​)

Find the numerical value of $P _ { 4 } ^ { 6 }$ .

$\mathrm { P } _ { 4 } ^ { 10 }$

$\left( \begin{array} { l } 90 \\90\end{array} \right)$

$\left( \begin{array} { c } 70 \\0\end{array} \right)$

$\mathrm { P } _ { 4 } ^ { 8 }$

Find the numerical value of $P \frac { 5 } { 5 }$ .

Which expression is equivalent to $P _ { n } ^ { N }$ ? A) $\frac { N ! } { ( N - n ) ! }$ B) $\frac { N ! } { n ! }$ C) $\frac { N ! } { n ! ( N - n ) ! }$ D) $\frac { N ! n ! } { ( N - n ) ! }$

$\left( \begin{array} { l } 70 \\68\end{array} \right)$

$\mathrm { P } _ { 0 } ^ { 12 }$

$\left( \begin{array} { l } 9 \\4\end{array} \right)$