Chapter 8, Problem 63CR

(a)

To determine

To find: The number of ways in which the sum of the number is 12 with replacement_.

Answer to Problem 63CR

The total of 12 occurs in 11 different ways.

Explanation of Solution

Given:

The given statement is that slip of paper numbered 1 through 15 are placed in a hat.

Calculation:

Consider the possible pair of sum is,

  $\begin{array}{l}\text{First:1}234567891011\\ \text{Second:11}10987654321\end{array}$

From the list it is seen that the total of 12 occurs in 11 different ways.

(b)

To determine

To find: The number of ways in which the sum of the number is 12 with no replacement_.

Answer to Problem 63CR

The list has no replacement then $\left(6,6\right)$ is not possible so it is removed.

Explanation of Solution

Given:

The given statement is that slip of paper numbered 1 through 15 are placed in a hat.

Calculation:

Consider the possible pair of sum is,

  $\begin{array}{l}\text{First:1}234567891011\\ \text{Second:11}10987654321\end{array}$

From the list as there is no replacement then $\left(6,6\right)$ is not possible so it is removed.