﻿ Permutations and Combinations Worksheet - Page 12 | Problems & Solutions # Permutations and Combinations Worksheet - Page 12

Permutations and Combinations Worksheet
• Page 12
111.
What is the value of $\frac{4!+3!}{4!-3!}$? a. $\frac{4}{3}$ b. $\frac{7}{5}$ c. $\frac{5}{3}$ d. $\frac{6}{4}$

#### Solution:

4! = 4 ×3 ×2 ×1 = 24
[Expand 4! and multiply.]

3! = 3 ×2 ×1 = 6
[Expand 3! and multiply.]

4! + 3! = 24 + 6 = 30
[Substitute the values of 4! and 3!.]

4! - 3! = 24 - 6 = 18
[Substitute the values of 4! and 3!.]

4!+3!4!-3! = 3018
[Substitute the values of (4! + 3!) and (4! - 3!).]

4!+3!4!-3! = 53
[Simplify the fraction.]

The value of 4!+3! / 4!-3! is 5 / 3.

112.
Henry lists different arrangements of the letters in the word $\mathrm{NKP}$ as follows: $\mathrm{NPK}$, $\mathrm{NKP}$, $\mathrm{PKN}$, $\mathrm{PNK}$, and $\mathrm{KPN}$. Find the number of arrangements not included in the list. a. 1 b. 2 c. 8 d. 3

#### Solution:

Total number of letters in the word NKP = 3

= 3! = 3 x 2 x 1 = 6
Total number of arrangements formed by all the letters of the word NKP
[Expand 3! and multiply]

Total number of arrangements listed = 5

Number of arrangements not included in the list = 6 - 5 = 1
[Subtract.]