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Evaluate : (i) (12!)/(10!) (ii) (14...

Evaluate :
`(i) (12!)/(10!)`
(ii) `(14!)/(10!5!)`
`(iii) (1)/(4!)+(1)/(5!)+(1)/(6!)+(1)/(7!)`

Text Solution

Verified by Experts

(i) `(12xx11xx10!)/(10!)" "(because n! ""=n(n-1)(n-2)!)`
`=132`
(ii) `(14!)/(10!5!)`
`=(14xx13xx12xx11xx10!)/(10!(5xx4xx3xx2xx1))`
`=(14xx13xx12xx11)/(5xx4xx3xx2xx1)`
`=(7xx13xx11)/(5)=(1001)/(5)`
(iii) `(1)/(4!)+(1)/(5!)+(1)/(6!)+(1)/(7!)`
`=(7xx6xx5)/(7xx6xx5xx4!)+(7xx6)/(7xx6xx5!)+(7)/(7xx6!)+(1)/(7!)`
`=(210)/(7!)+(42)/(7!)+(7)/(7!)+(1)/(7!)`
`=(210+42+7+1)/(7!)=(260)/(7!)`
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