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The least value of natural number n such...

The least value of natural number n such that `((n-1),(5))+((n-1),(6))lt((n),(r))," where"((n),(r))=(n!)/((n-r)!r!),is `

A

12

B

13

C

14

D

15

Text Solution

Verified by Experts

The correct Answer is:
C
`.^(n-1)C_(5)+.^(n-1)C_(6)lt.^(n)C_(7)`
`.^(n)C_(6)lt.^(n)C_(7)`
`(n!)/(6!(n-6)!)lt(n!)/(7!(n-7)!)`
`n-6gt7`
`ngt13`
`.^(n)"min"=14`
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