Six fair dice are thrown independently. The probability that three are exactly `2` different pairs (A pair is an ordered combination like `2,2,1,3,5,6

Question

Six fair dice are thrown independently. The probability that three are exactly `2` different pairs (A pair is an ordered combination like `2,2,1,3,5,6

Six fair dice are thrown independently. The probability that three are exactly `2` different pairs (A pair is an ordered combination like `2,2,1,3,5,6`) is
A. `5//72`
B. `26//72`
C. `125//144`
D. `5//36`

Monjur Alahi

9 views

2025-01-04 04:42

1 Answers

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Salim Ahmed Kawsar · Accepted Answer · 2023-02-05T15:29:48+06:00

Correct Answer - B
`(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))=(26)/(72)`