Question

Out of 6 boys 4 girls a commitee of 5 has to be formed. In how many ways can it be done if 2 girls are to be included in the commitee

Answer 1

Answer:

120 ways.

Step-by-step explanation:

We are given total of 6 boys and 4 girls and we have to form a committee of 5 candidates from which two are girls.

Total number of ways of selecting 5 people from total of 10 people (6 + 4 )

       =    $^{10} C_5$

Number of ways of selecting 2 girls from total of 4 girls and then the remaining 3 people from 6 boys = $^{4} C_2$ x $^{6} C_3$  = $\frac{4!}{2!\times 2!}\times \frac{6!}{3!\times 3!}$

                                                            { because $^{n}C_r = \frac{n!}{r!*(n-r)!}$ }

                                                   = 120 ways.

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