## NCERT Solutions for Class 11 Maths Chapter 7 Permutations and Combinations Exercise 7.2

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1. Evaluate:

(i) 8 !

(ii) 4! - 3!

(i) 8! = 8 Ã— 7 Ã— 6 Ã— 5 Ã— 4 Ã— 3 Ã— 2Ã—Â 1

= 40320

(ii) 4! = 4 Ã— 3 Ã— 2 Ã— 1 = 24

3! = 3 Ã— 2 Ã— 1 = 6

4! â€“ 3! = 24 â€“ 6 = 18

2.Â Is 3! + 4!= 7!?

3! = 3 Ã— 2Ã— 1 = 6

4! = 4 Ã— 3 Ã— 2 Ã— 1 = 24

LHS = 3! + 4! = 6 + 24 = 30

RHS = 7! = 7Ã—Â 6 Ã— 5 Ã— 4 Ã— 3 Ã— 2 Ã— 1 = 5040

LHS = RHS

3.Â Compute 8!/(6! Ã— 2!)

8!/(6! Ã— 2!) = (8Ã— 7 Ã— 6 Ã— 5 Ã— 4 Ã— 3 Ã— 2 Ã— 1)/((6 Ã— 5 Ã— 4 Ã— 3 Ã— 2 Ã— 1) Ã— ( 2 Ã— 1))

= (8 Ã— 7)/(2 Ã— 1) = 28

4.Â If 1/6! + 1/7!Â = x/8! , find x.

1/6! + 1/7! = 1/6! + 1/7.6! = x/(8.7.6. !)

=> 1/6! (1 + 1/7) = x/(8.7.6. !)

=> 8/7 = x/8.7 => x = 64

5. Evaluate n!/(n â€“ r) when

(i) n = 6, r = 2

(ii) n = 9, r = 5

(i) n = 6, r = 2

n!/(n â€“ r)! = 6!/(6 â€“ r) ! = 6!/4!

= (6 Ã— 5 Ã— 4 Ã— 3Ã— 2 Ã— 1)/(4 Ã— 3 Ã— 2 Ã— 1) = 6 Ã— 5 = 30

(ii) n = 9, r = 5

n!/(n â€“ r)! = 9! /(9 â€“ 5)!Â = 9! /4!

= (9 Ã—Â 8 Ã— 7 Ã— 6 Ã— 5 Ã— 4 Ã— 3 Ã— 2 Ã— 1)/(4 Ã— 3 Ã— 2 Ã— 1)

9 Ã— 8 Ã— 7 Ã— 6 Ã— 5 = 15120

1. Evaluate:

(i) 8 !

(ii) 4! - 3!

**Answer**(i) 8! = 8 Ã— 7 Ã— 6 Ã— 5 Ã— 4 Ã— 3 Ã— 2Ã—Â 1

= 40320

(ii) 4! = 4 Ã— 3 Ã— 2 Ã— 1 = 24

3! = 3 Ã— 2 Ã— 1 = 6

4! â€“ 3! = 24 â€“ 6 = 18

2.Â Is 3! + 4!= 7!?

**Answer**3! = 3 Ã— 2Ã— 1 = 6

4! = 4 Ã— 3 Ã— 2 Ã— 1 = 24

LHS = 3! + 4! = 6 + 24 = 30

RHS = 7! = 7Ã—Â 6 Ã— 5 Ã— 4 Ã— 3 Ã— 2 Ã— 1 = 5040

LHS = RHS

3.Â Compute 8!/(6! Ã— 2!)

**Answer**8!/(6! Ã— 2!) = (8Ã— 7 Ã— 6 Ã— 5 Ã— 4 Ã— 3 Ã— 2 Ã— 1)/((6 Ã— 5 Ã— 4 Ã— 3 Ã— 2 Ã— 1) Ã— ( 2 Ã— 1))

= (8 Ã— 7)/(2 Ã— 1) = 28

4.Â If 1/6! + 1/7!Â = x/8! , find x.

**Answer**1/6! + 1/7! = 1/6! + 1/7.6! = x/(8.7.6. !)

=> 1/6! (1 + 1/7) = x/(8.7.6. !)

=> 8/7 = x/8.7 => x = 64

5. Evaluate n!/(n â€“ r) when

(i) n = 6, r = 2

(ii) n = 9, r = 5

**Answer**(i) n = 6, r = 2

n!/(n â€“ r)! = 6!/(6 â€“ r) ! = 6!/4!

= (6 Ã— 5 Ã— 4 Ã— 3Ã— 2 Ã— 1)/(4 Ã— 3 Ã— 2 Ã— 1) = 6 Ã— 5 = 30

(ii) n = 9, r = 5

n!/(n â€“ r)! = 9! /(9 â€“ 5)!Â = 9! /4!

= (9 Ã—Â 8 Ã— 7 Ã— 6 Ã— 5 Ã— 4 Ã— 3 Ã— 2 Ã— 1)/(4 Ã— 3 Ã— 2 Ã— 1)

9 Ã— 8 Ã— 7 Ã— 6 Ã— 5 = 15120