Question

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Updated on : 2022-09-05

Solution

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Correct option is A)

Total number of girls in the group $=4$

Total number of boys in the group $=7$

Probability of selecting atleast one boy and one girl =?

By considering following ways we can select

i) $1$ girls $+4$ boys $⇒_{4}C_{1}×_{7}C_{4}$

ii) $2$ girls $+3$ boys $⇒_{4}C_{2}×_{7}C_{3}$

iii) $3$ girls $+2$ boys $⇒_{4}C_{3}×_{7}C_{2}$

iv) $4$ girls $+1$ boy $⇒_{4}C_{4}×_{7}C_{1}$

Total number of ways $=(_{4}C_{1}×_{7}C_{4})+(_{4}C_{2}×_{7}C_{3})+(_{4}C_{3}×_{7}C_{2})+(_{4}C_{4}×_{7}C_{1})$

$=140+210+84+7$

$=441$

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