Previous exercise – Permutation and Combination – Exercise 4.2
Permutation and Combination – Exercise 4.3
- 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
- Evaluate
(i) 6!
(ii) 9!
(iii) 8! – 5!
(iv) 7!/5!
(v) 12!/(9!)(3!)
(vi) 30!/80!
- Evaluate
(i) n!/(n-r)!
(ii) n!/(n – r)!r! when n = 15 and r = 2
- Find the LCM of 4! , 5! , 6!
- If (n+1)! = 12(n – 1)!, find the value of n
Permutation and Combination – Exercise 4.3 – Solutions:
- 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!
- 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
- 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
- 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
- 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
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