# Permutation and Combination – Exercise 4.3 – Class X

Previous exercise – Permutation and Combination – Exercise 4.2

#### Permutation and Combination – Exercise 4.3

1. Convert the following products into factorials.

(i)1 x 2 x 3 x 4 x 5 x 6 x 7

(ii) 18 x 17 … x 3 x 2 x 1

(iii) 6 x 7 x 8 x 9

(iv) 2 x 4 x 6 x 8

1. Evaluate

(i) 6!

(ii) 9!

(iii) 8! – 5!

(iv) 7!/5!

(v) 12!/(9!)(3!)

(vi) 30!/80!

1. Evaluate

(i) n!/(n-r)!

(ii) n!/(n – r)!r!  when n = 15 and r = 2

1. Find the LCM of 4! , 5! , 6!
2. If (n+1)! = 12(n – 1)!, find the value of n

#### Permutation and Combination – Exercise 4.3 – Solutions:

1. Convert the following products into factorials.

(i)1 x 2 x 3 x 4 x 5 x 6 x 7

(ii) 18 x 17 … x 3 x 2 x 1

(iii) 6 x 7 x 8 x 9

(iv) 2 x 4 x 6 x 8

Solution:

(i)1 x 2 x 3 x 4 x 5 x 6 x 7 = 7!

(ii) 18 x 17 … x 3 x 2 x 1 = 18!

(iii) 6 x 7 x 8 x 9 = 9!/5!

(iv) 2 x 4 x 6 x 8 = 384 = 16*24 = 16*4!

1. Evaluate

(i) 6!

(ii) 9!

(iii) 8! – 5!

(iv) 7!/5!

(v) 12!/(9!)(3!)

(vi) 30!/80!

Solution:

(i) 6! = 1 x 2 x 3 x 4 x 5 x 6 = 720

(ii) 9! = 362880

(iii) 8! – 5! = 40200

(iv) 7!/5! = 1x2x3x4x5x6x7/1x2x3x4x5 = 6 x 7 = 42

(v) 12!/(9!)(3!) = 1x2x3x4x5x6x7x8x9x10x11x12/(1x2x3x4x5x6x7x8x9)(1x2x3) = 10x11x12/1x2x3 = 5x11x4 = 220

(vi) 30!/28!  = 28! 29*30/28! = 29 * 30 = 870

1. Evaluate

(i) n!/(n-r)! when n = 15 and r = 2

(ii) n!/(n – r)!r!  when n = 15 and r = 2

Solution:

(i) n!/(n-r)! when n = 15 and r = 2

n!/(n-r)!  = 15!/(15 – 2)! = 15!/13! = 210

(ii) n!/(n – r)!r!  when n = 15 and r = 2

n!/(n – r)!r!  = 15!/(15-2)!2! = 15!/(13)!2! = 105

1. Find the LCM of 4! , 5! , 6!

Solution:

4! = 1 x 2 x 3 x 4

5! = 1 x 2 x 3 x 4 x 5

6! = 1 x 2 x 3 x 4 x 5 x 6

Therefore, LCM of 4! , 5! and 6! is 720

1. If (n+1)! = 12(n – 1)!, find the value of n

Solution:

(n+1)! = 12(n – 1)!

(n – 1)! x n x (n + 1) = 12 x (n – 1)!

n(n+1) = 12

n2 + n = 12

n2 + n – 12 = 0

n2 + 4n – 3n – 12 = 0

n(n + 4) – 3(n + 4) = 0

(n – 3)(n + 4) = 0

n – 3 = 0 or n + 4 = 0

n = +3 or n = – 4

Next Exercise Permutation and Combination – Exercise 4.4