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Permutations and Combinations Worksheet - Page 12

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


Correct answer : (3)
 112.  
Henry lists different arrangements of the letters in the word NKP as follows: NPK, NKP, PKN, PNK, and 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.]


Correct answer : (1)

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