Chapter 13.2, Problem 36E

(a)

To determine

To find: The number of ways to arrange the letters “calculating.”

Answer to Problem 36E

The number of arrangements are $4,989,600$ .

Explanation of Solution

Given:

The phrase is “calculating rules.”

Calculation:

There are 11 letters in calculating that are 2-C, 2-A, 2-L.

This is the permutation with repetition of $11$ elements.

The possible numbers of arrangements are as follows.

  $\frac{11!}{2!2!2!}=4,989,600$

Therefore, the number of arrangements are $4,989,600$ .

(b)

To determine

To rearrange: The letters and the space in the phrase to form the name of a branch of mathematics.

Answer to Problem 36E

The rearranged phrase is “integral calculus.”

Explanation of Solution

Given:

The phrase is “calculating rules.”

Calculation:

The letter can be arranged as “integral calculus.”

Therefore, the rearranged phrase is “integral calculus.”