Help Please!!!

Question

+13

662

1

+1072

Let n and k be positive integers such that

Find the smallest possible value of n.

geno3141 · Answer 1 · 2020-03-06T11:40:32

_nC_{k / n}C_{k+1 = 4 / 11}

_nC_k = n! / [ k! · (n - k)! ] _nC_k+1= n! / [ (k + 1)! · ( n - (k + 1) )! ] ---> _nC_k+1= n! / [ (k + 1)! · (n - k - 1)! ]

_nC_{k / n}C_k+1= n! / [ k! · (n - k)! ] / [ n! / [ (k + 1)! · (n - k - 1)! ] ]

= [ n! · (k + 1)! · ( n - k - 1) )! ] / [ k! · (n - k)! · n! ]

= (k + 1) / (n - k)

But (k + 1) / (n - k) = 4 / 11

---> k + 1 = 4 ---> k = 3

---> n - k = 11 ---> n - 3 = 11 ---> n = 14