Seven girls `G_(1), G_(2), G_(3)`, …, `G_(7)` are such that their ages are in order `G_(1) lt G_(2) lt G_(3) lt … lt G_(7)`. Five girls are selected at random and arranged in increasing order of their ages. The probability that `G_(5)` and `G_(7)` are not consecutive is

Options

A. `(20)/(21)`
B. `(19)/(21)`
C. `(17)/(21)`
D. `(13)/(21)`

Answer

C

Explanation

Required probability = 1 - P (`G_(5)` and `G_(7)` are consecutive)
`= 1 - (.^(4)C_(3))/(.^(7)C_(5)) = (17)/(21)`