Question

In a group of 15 boys there are 7 boy scouts. In how many ways 12 boys can be selected so as to include exactly 6 boy's scouts

Answer 1

SOLUTION

GIVEN

In a group of 15 boys there are 7 boy scouts.

TO DETERMINE

The number of ways 12 boys can be selected so as to include exactly 6 boy's scouts

EVALUATION

Total number of boys in the group = 15

Among which 7 boy scouts

We have to select 12 boys

Among 12 boys exactly 6 boy's scouts

So 6 Boy's scouts are to selected from 7 boy scouts

and rest ( 12 - 6) = 6 to be selected from ( 15 - 7) = 8 boys

So the required number of ways

$\sf{ = {}^{7}C_6 \: \times \: {}^{8}C_6 }$

$= \displaystyle \sf{ \frac{7!}{6! \: 1!} \times \frac{8!}{6! \: 2!}}$

$= 7 \times 28$

$= 196$

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