Chapter 9.1, Problem 49E

Solution

a.

To state: A counting problem for the number $C_{{52}_3}$ .

The resultant problem is “Find the number of ways of selecting 3 cards from the standard deck of cards.”

Given information:

The given number is $C_{{52}_3}$ .

Explanation:

Consider the given number $C_{{52}_3}$ and form a counting problem.

Let’s take standard card consisting 52 cards.

Now the number of selecting 3 cards out of 52 cards is $C_{{52}_3}$ .

Then the problem is “Find the number of ways of selecting 3 cards from the standard deck of cards.”

b.

To state: A counting problem for the number $C_{{12}_3}$ .

The resultant problem is “Find the number of ways of selecting 3 candidates from the available 12 candidates.”

Given information:

The given number is $C_{{12}_3}$ .

Explanation:

Consider the given number $C_{{12}_3}$ and form a counting problem.

Then the problem is “Find the number of ways of selecting 3 candidates from the available 12 candidates.”

c.

To state: A counting problem for the number $P_{{25}_{11}}$ .

The resultant problem is “Find the number of arrangements of 11 books from 25 books.”

Given information:

The given number is $P_{{25}_{11}}$ .

Explanation:

Consider the given number $P_{{25}_{11}}$ and form a counting problem.

Then the problem is “Find the number of arrangements of 11 books from 25 books.”

d.

To state: A counting problem for the number $2^5$ .

The resultant problem is “In how many ways a student can answer a true and false questions if there are 5 questions in a test.”

Given information:

The given number is $2^5$ .

Explanation:

Consider the given number $2^5$ and form a counting problem.

Let’s take standard card consisting 52 cards.

Now the number of selecting 3 cards out of 52 cards is $C_{{52}_3}$ .

Then the problem is “In how many ways a student can answer a true and false questions if there are 5 questions in a test.”

e.

To state: A counting problem for the number $3\cdot 2^{10}$ .

The resultant problem is “Find the number of different license plates with first character being an alphabet from A , B , and C and 10 digits each digit is either 1 or 2.”

Given information:

The given number is $3\cdot 2^{10}$ .

Explanation:

Consider the given number $3\cdot 2^{10}$ and form a counting problem.

Then the problem is “Find the number of different license plates with first character being an alphabet from A , B , and C and 10 digits each digit is either 1 or 2.”