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!
Answer
(i) 8! = 8 × 7 × 6 × 5 × 4 × 3 × 2× 1
= 40320
(ii) 4! = 4 × 3 × 2 × 1 = 24
3! = 3 × 2 × 1 = 6
4! – 3! = 24 – 6 = 18
2. Is 3! + 4!= 7!?
Answer
3! = 3 × 2× 1 = 6
4! = 4 × 3 × 2 × 1 = 24
LHS = 3! + 4! = 6 + 24 = 30
RHS = 7! = 7× 6 × 5 × 4 × 3 × 2 × 1 = 5040
LHS = RHS
3. Compute 8!/(6! × 2!)
Answer
8!/(6! × 2!) = (8× 7 × 6 × 5 × 4 × 3 × 2 × 1)/((6 × 5 × 4 × 3 × 2 × 1) × ( 2 × 1))
= (8 × 7)/(2 × 1) = 28
4. If 1/6! + 1/7! = 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 – r) when
(i) n = 6, r = 2
(ii) n = 9, r = 5
Answer
(i) n = 6, r = 2
n!/(n – r)! = 6!/(6 – r) ! = 6!/4!
= (6 × 5 × 4 × 3× 2 × 1)/(4 × 3 × 2 × 1) = 6 × 5 = 30
(ii) n = 9, r = 5
n!/(n – r)! = 9! /(9 – 5)! = 9! /4!
= (9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1)/(4 × 3 × 2 × 1)
9 × 8 × 7 × 6 × 5 = 15120
1. Evaluate:
(i) 8 !
(ii) 4! - 3!
Answer
(i) 8! = 8 × 7 × 6 × 5 × 4 × 3 × 2× 1
= 40320
(ii) 4! = 4 × 3 × 2 × 1 = 24
3! = 3 × 2 × 1 = 6
4! – 3! = 24 – 6 = 18
2. Is 3! + 4!= 7!?
Answer
3! = 3 × 2× 1 = 6
4! = 4 × 3 × 2 × 1 = 24
LHS = 3! + 4! = 6 + 24 = 30
RHS = 7! = 7× 6 × 5 × 4 × 3 × 2 × 1 = 5040
LHS = RHS
3. Compute 8!/(6! × 2!)
Answer
8!/(6! × 2!) = (8× 7 × 6 × 5 × 4 × 3 × 2 × 1)/((6 × 5 × 4 × 3 × 2 × 1) × ( 2 × 1))
= (8 × 7)/(2 × 1) = 28
4. If 1/6! + 1/7! = 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 – r) when
(i) n = 6, r = 2
(ii) n = 9, r = 5
Answer
(i) n = 6, r = 2
n!/(n – r)! = 6!/(6 – r) ! = 6!/4!
= (6 × 5 × 4 × 3× 2 × 1)/(4 × 3 × 2 × 1) = 6 × 5 = 30
(ii) n = 9, r = 5
n!/(n – r)! = 9! /(9 – 5)! = 9! /4!
= (9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1)/(4 × 3 × 2 × 1)
9 × 8 × 7 × 6 × 5 = 15120