`10` different books and `2` different pens are given to `3` boys so that each gets equal number of things. The probability that the same boy does not

Monjur Alahi

`10` different books and `2` different pens are given to `3` boys so that each gets equal number of things. The probability that the same boy does not receive both the pens is
A. `5//11`
B. `7//11`
C. `9//11`
D. `6//11`


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Salim Ahmed Kawsar

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Correct Answer - C
`(c )` `m(S)=(12!)/(4!4!4!3!)3!=(12!)/(4!4!4!)`
`n(E)=` the number of ways in which any one boy gets both the pens
`="^(3)C_(1)^(10)C_(2)(8!)/(4!4!2!)2!=3xx45(8!)/(4!4!)`
`:.P(E)=(3xx45(8!)/(4!4!))/((12!)/(4!4!4!))=(2)/(11)`
`:.` Required probability `=1-(2)/(11)=(9)/(11)`

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