TOPICS

Exercise - 7.2

Permutations and Combinations

**Question-1 :-** Evaluate:

(i) 8 !

(ii) 4 ! – 3 !

(i) 8! = 1 × 2 × 3 × 4 × 5 × 6 × 7 × 8 = 40320 (ii) 4! = 1 × 2 × 3 × 4 = 24 3! = 1 × 2 × 3 = 6 Therefore, 4! – 3! = 24 – 6 = 18

**Question-2 :-** Is 3 ! + 4 ! = 7 ! ?

3! = 1 × 2 × 3 = 6 4! = 1 × 2 × 3 × 4 = 24 Therefore, 3! + 4! = 6 + 24 = 30 Now, 7! = 1 × 2 × 3 × 4 × 5 × 6 × 7 = 5040 Therefore, 3! + 4! ≠ 7!

**Question-3 :-** Compute: 8!/6!2! .

8!/6!2! = (8 x 7 x 6!)/(6! x 2 x 1) = (8 x 7)/2 = 4 x 7 = 28

**Question-4 :-** If 1/6! + 1/7! = x/8!, find x.

1/6! + 1/7! = x/8! 1/6! + 1/(7 x 6!) = x/(8 x 7 x 6!) 1 + 1/7 = x/56 8/7 = x/56 x = (8 x 56)/7 x = 8 x 8 x = 64

**Question-5 :-** Evaluate n!/(n-r)! , when

(i) n = 6, r = 2

(ii) n = 9, r = 5.

(i) When, n = 6, r = 2 n!/(n-r)! = 6!/(6-2)! = 6!/4! = (6 x 5 x 4!)/4! = 6 x 5 = 30

(ii) When, n = 9, r = 5 n!/(n-r)! = 9!/(9-5)! = 9!/4! = (9 x 8 x 7 x 6 x 5 x 4!)/4! = 9 x 8 x 7 x 6 x 5 = 15120

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