KVPY SA Exam 19-Nov-2017 Question Paper

Question : 14 of 80

Marks: +1, -0

The least value of a natural number n such that

({n-1}/5)+({n-1}/6<(n/7)

, where

(n /r)=n!/ {(n-r )! r!}

, is

Solution:

^{n–1}C_5 + ^{n–1}C_6 < ^{n}C_7

^nC_6 < ^nC_7

$n!/{6!(n -6)!}n – 6 > 7
n > 13

n_\min = 14

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