A bag contains 50 balls numbered 1,2,3...,50.

Five balls are removed at random without replacement.Then chance that the number on 5th ball is smaller than the number on 3rd ball and the number on the 3rd ball is smaller than the number on the 1st ball is?

a)1/2

b)1/4

c)5/8

d)1/6

1 2 3 4 5
_ _ _ _ _

There is restriction on 1 3 5 place. So first we will select 3 numbers from 50 numbers and these can be arranged only in 1 way such that number at 1 position smaller than number at 3^rd position and number at 3^rd position is smaller than number at 5^th position ( You can verify it by chosing 3 numbers and try possible araangements and observe one arrangement will satisfy the condition)
No of ways to this is ⁵⁰C₃
No for remaining 2 positions no of ways of arranging will be ⁴⁷C₂ x2!
No of possible ways is ⁵⁰C₃x ⁴⁷C₂ x2!
Total arrangement possible is ⁵⁰P₅
Required probability can be found using simplication of above two and answer will be 1/6