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Six fair dice are thrown independently. ...

Six fair dice are thrown independently. The probability that three are exactly `2` same pairs (A pair is an ordered combination like `1,1,2,2,3,4`) is

A

`5//72`

B

`26//72`

C

`125//144`

D

`25//36`

Text Solution

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The correct Answer is:
D
`(b)` Total no of outcomes `=6^(6)`
Number of ways of choosing `4` other different numbers is `"^(6)C_(2)` and choosing `2` out of remaining `4` can be lone in `"^(4)C_(2)` ways. Also numbr of ways of arranging `6` numbers of which `2` are alike and `2` are alike is `(6!)/(2!2!)`
`:.` Required probability `=("^(6)C_(2)xx^(4)C_(2)xx(6)/(2!2!))/(6^(6))=(25)/(36)`
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