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Evaluate (n!)/((n-r)!), when (i) n = ...

Evaluate `(n!)/((n-r)!)`, when
(i) `n = 6, r = 2` (ii) `n = 9, r = 5`

Text Solution

Verified by Experts

(i) `:' n = 6` and `r = 2`
`(lfloorn)/(ul(n-r)) = (lfloor6)/(ul(6-2)) = (lfloor6)/(lfloor4) = (6 xx 5 xx lfloor4)/(lfloor4) = 6 xx 5 = 30`
Therefore, `(lfloorn)/(ul(n-r)) = 30`
(ii) `:' n = 9` and `r = 5`
`(lfloorn)/(ul(n-r)) (lfloor9)/(ul(9-5)) = (lfloor9)/(lfloor4)`
`= (9 xx 8 xx 7 xx 6 xx 5 xx 4 xx 3 xx 2 xx 1)/(4 xx 3 xx 2 xx 1)`
`= 89 xx 8 xx 7 xx 6 xx 5 = 15120`.
Therefore, `(lfloorn)/(ul(n-r)) = 15120`
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