Question 1

Using the ordinary alphabet and allowing repeated letters, ﬁnd the number of words of length 8 that begin and end with T.

Accepted Answer

The answer of Using the ordinary alphabet and allowing repeated...

Question 2

suppose you have a class with 30 students-10 freshmen, 12 sophomores, and 8 juniors.
-In how many ways can you get a committee of 4 freshmen and 3 sophomores?

Accepted Answer

The answer of suppose you have a class with 30...

Question 3

How many ways are there to select 6 students from a class of 25 to hold six diﬀerent executive positions on

Accepted Answer

The answer of How many ways are there to select...

Question 4

How many subsets with an odd number of elements does a set with 10 elements have?

Accepted Answer

The answer of How many subsets with an odd number...

Question 5

How many subsets with more than two elements does a set with 100 elements have?

Accepted Answer

The answer of How many subsets with more than two...

Question 6

Using the ordinary alphabet and allowing repeated letters, ﬁnd the number of words of length 8.

Accepted Answer

The answer of Using the ordinary alphabet and allowing repeated...

Question 7

Using the ordinary alphabet and allowing repeated letters, ﬁnd the number of words of length 8 that begin and end with the same letter.

Accepted Answer

The answer of Using the ordinary alphabet and allowing repeated...

Question 8

Make up a word problem in good English whose answer is $$15 ! / 10 !$$

Accepted Answer

The answer of Make up a word problem in good...

Question 9

Using the ordinary alphabet and allowing repeated letters, ﬁnd the number of words of length 8 that have exactly one B.

Accepted Answer

The answer of Using the ordinary alphabet and allowing repeated...

Question 10

suppose you have a class with 30 students-10 freshmen, 12 sophomores, and 8 juniors.
-In how many ways can you put all students in a line so that the freshmen are ﬁrst, the sophomores are in the middle, and the juniors are at the end?

Accepted Answer

The answer of suppose you have a class with 30...

Question 11

let A be the set of all strings of decimal digits of length ﬁve. For example, 00312 and 19483
are strings in A.
-How many strings in A have exactly one 5?

Accepted Answer

The answer of let A be the set of all...

Question 12

Each user has a password 6 characters long where each character is an uppercase letter, a lowercase letter, or a digit. Each password must contain at least one digit. How long will it take to check every possible character combination, if each check takes one unit of time.

Accepted Answer

The answer of Each user has a password 6 characters...

Question 13

Using the ordinary alphabet and allowing repeated letters, ﬁnd the number of words of length 8 that begin with L or end with R.

Accepted Answer

The answer of Using the ordinary alphabet and allowing repeated...

Question 14

suppose you have a class with 30 students-10 freshmen, 12 sophomores, and 8 juniors.
-In how many ways can you put all 30 in a line?

Accepted Answer

The answer of suppose you have a class with 30...

Question 15

Make up a word problem in good English whose answer is $\left( \begin{array} { c } 
15 \
4
\end{array} \right) \cdot \left( \begin{array} { l } 
7 \
3
\end{array} \right)$

Accepted Answer

The answer of Make up a word problem in good...

Question 16

How many ways are there to select 6 students from a class of 25 to serve on a committee?

Accepted Answer

The answer of How many ways are there to select...

Question 17

Find the number of subsets of S = {1, 2, 3, . . . , 10} that contain neither 5 nor 6.

Accepted Answer

The answer of Find the number of subsets of S...

Question 18

let A be the set of all strings of decimal digits of length ﬁve. For example, 00312 and 19483
are strings in A.
-How many strings in A have exactly three 5s?

Accepted Answer

The answer of let A be the set of all...

Question 19

Using the ordinary alphabet and allowing repeated letters, ﬁnd the number of words of length 8 that have at least one C.

Accepted Answer

The answer of Using the ordinary alphabet and allowing repeated...

Question 20

suppose you have a class with 30 students-10 freshmen, 12 sophomores, and 8 juniors.
-In how many ways can you get a committee of 7?

Accepted Answer

The answer of suppose you have a class with 30...

Quiz 6: A: Counting

Using the ordinary alphabet and allowing repeated letters, ﬁnd the number of words of length 8 that begin and end with T.

suppose you have a class with 30 students-10 freshmen, 12 sophomores, and 8 juniors. -In how many ways can you get a committee of 4 freshmen and 3 sophomores?

How many ways are there to select 6 students from a class of 25 to hold six diﬀerent executive positions on

How many subsets with an odd number of elements does a set with 10 elements have?

How many subsets with more than two elements does a set with 100 elements have?

Using the ordinary alphabet and allowing repeated letters, ﬁnd the number of words of length 8.

Using the ordinary alphabet and allowing repeated letters, ﬁnd the number of words of length 8 that begin and end with the same letter.

Make up a word problem in good English whose answer is $15 ! / 10 !$

Using the ordinary alphabet and allowing repeated letters, ﬁnd the number of words of length 8 that have exactly one B.

suppose you have a class with 30 students-10 freshmen, 12 sophomores, and 8 juniors. -In how many ways can you put all students in a line so that the freshmen are ﬁrst, the sophomores are in the middle, and the juniors are at the end?

let A be the set of all strings of decimal digits of length ﬁve. For example, 00312 and 19483 are strings in A. -How many strings in A have exactly one 5?

Each user has a password 6 characters long where each character is an uppercase letter, a lowercase letter, or a digit. Each password must contain at least one digit. How long will it take to check every possible character combination, if each check takes one unit of time.

Using the ordinary alphabet and allowing repeated letters, ﬁnd the number of words of length 8 that begin with L or end with R.

suppose you have a class with 30 students-10 freshmen, 12 sophomores, and 8 juniors. -In how many ways can you put all 30 in a line?

Make up a word problem in good English whose answer is $\left( \begin{array} { c } 15 \\4\end{array} \right) \cdot \left( \begin{array} { l } 7 \\3\end{array} \right)$

How many ways are there to select 6 students from a class of 25 to serve on a committee?

Find the number of subsets of S = {1, 2, 3, . . . , 10} that contain neither 5 nor 6.

let A be the set of all strings of decimal digits of length ﬁve. For example, 00312 and 19483 are strings in A. -How many strings in A have exactly three 5s?

Using the ordinary alphabet and allowing repeated letters, ﬁnd the number of words of length 8 that have at least one C.

suppose you have a class with 30 students-10 freshmen, 12 sophomores, and 8 juniors. -In how many ways can you get a committee of 7?

Quiz 6: A: Counting

Using the ordinary alphabet and allowing repeated letters, ﬁnd the number of words of length 8 that begin and end with T.

suppose you have a class with 30 students-10 freshmen, 12 sophomores, and 8 juniors. -In how many ways can you get a committee of 4 freshmen and 3 sophomores?

How many ways are there to select 6 students from a class of 25 to hold six diﬀerent executive positions on

How many subsets with an odd number of elements does a set with 10 elements have?

How many subsets with more than two elements does a set with 100 elements have?

Using the ordinary alphabet and allowing repeated letters, ﬁnd the number of words of length 8.

Using the ordinary alphabet and allowing repeated letters, ﬁnd the number of words of length 8 that begin and end with the same letter.

Make up a word problem in good English whose answer is 15!/10!15 ! / 10 !15!/10!

Using the ordinary alphabet and allowing repeated letters, ﬁnd the number of words of length 8 that have exactly one B.

suppose you have a class with 30 students-10 freshmen, 12 sophomores, and 8 juniors. -In how many ways can you put all students in a line so that the freshmen are ﬁrst, the sophomores are in the middle, and the juniors are at the end?

let A be the set of all strings of decimal digits of length ﬁve. For example, 00312 and 19483 are strings in A. -How many strings in A have exactly one 5?

Each user has a password 6 characters long where each character is an uppercase letter, a lowercase letter, or a digit. Each password must contain at least one digit. How long will it take to check every possible character combination, if each check takes one unit of time.

Using the ordinary alphabet and allowing repeated letters, ﬁnd the number of words of length 8 that begin with L or end with R.

suppose you have a class with 30 students-10 freshmen, 12 sophomores, and 8 juniors. -In how many ways can you put all 30 in a line?

Make up a word problem in good English whose answer is (154)⋅(73)\left( \begin{array} { c } 15 \\4\end{array} \right) \cdot \left( \begin{array} { l } 7 \\3\end{array} \right)(154​)⋅(73​)

How many ways are there to select 6 students from a class of 25 to serve on a committee?

Find the number of subsets of S = {1, 2, 3, . . . , 10} that contain neither 5 nor 6.

let A be the set of all strings of decimal digits of length ﬁve. For example, 00312 and 19483 are strings in A. -How many strings in A have exactly three 5s?

Using the ordinary alphabet and allowing repeated letters, ﬁnd the number of words of length 8 that have at least one C.

suppose you have a class with 30 students-10 freshmen, 12 sophomores, and 8 juniors. -In how many ways can you get a committee of 7?

Make up a word problem in good English whose answer is $15 ! / 10 !$

Make up a word problem in good English whose answer is $\left( \begin{array} { c } 15 \\4\end{array} \right) \cdot \left( \begin{array} { l } 7 \\3\end{array} \right)$