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!
- Compute 8!/(6!x2!)
Solution:
8!/(6!x2!) = 8x7x6!/6!x2x1 = 8×7/2 = 28
- 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
- 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
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