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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

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

Grade:12

1 Answers

Harsh Patodia IIT Roorkee
askIITians Faculty 907 Points
6 years ago
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 3rd position and number at 3rd position is smaller than number at 5th 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

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