Permutation and Combination – Class XI – Exercise 7.2

1: Evaluate

(i) 8!

(ii) 4! – 3!

Solution:

(i) 8! = 1 × 2 × 3 × 4 × 5 × 6 × 7 × 8 = 40320

(ii)4! = 1 × 2 × 3 × 4 = 24

3! = 1 × 2 × 3 = 6

4! – 3! = 24 – 6 = 18


2: Is 3! + 4! = 7!?

Solution:

3! = 1 × 2 × 3 = 6

4! = 1 × 2 × 3 × 4 = 24

3! + 4! = 6 + 24 = 30

7! = 1 × 2 × 3 × 4 × 5 × 6 × 7 = 5040

3! + 4! ≠ 7!


  1. Compute 8!/(6!x2!)

Solution:

8!/(6!x2!) = 8x7x6!/6!x2x1 = 8×7/2 = 28


  1. If 1/6! + 1/7! = 1/8! , find x.

Solution:

1/6! + 1/7! = 1/8!

1/6! = 1/7×6! = 1/8x7x6!

1/6! (1+ 1/7!) = 1/8x7x6!

1 + 1/7 = x/8×7

8/7 = x/8×7

x = 8x8x7/7

x = 64


  1. Evaluate n!/(n-r)! , when

(i) n = 6, r = 2

(ii) n = 9, r = 5

Solution:

(i) n = 6, r = 2

n!/(n-r)! = 6!/(6-2)! = 6!/4! = 6x5x4!/4! = 30

(ii) n = 9, r = 5

n!/(n-r)! = 9!/(9-5)! = 9!/4! = 9x8x7x6x5x4!/4! = 15120


 

 

 

Advertisements