Question

There are 15 boys and 10 girls in your class. A four member committee is to be formed from the students of your class. In how many ways this can be done if the committee consists at least three girls

Answer 1

the number of ways 3 girls can be chosen=10*9*8=720
the number of ways 1 boy could be chosen=15
number of ways a committee could be formed=720*15=10800

Answer 2

Answer:

There are 2010 ways to form the committee consists at least three girls

Step-by-step explanation:

No. of boys = 15

No. of girls = 10

A four member committee is to be formed from the students of your class.

We are given that there should be at least 3 girls (i.e. 3 or more girls)

We will use combination  

Formula : $^nC_r=\frac{n!}{r!(n-r)!}$

Committee with 3 girls and 1 boy

No. of ways of forming  with 3 girls and 1 boy =$^{15}C_1 \times ^{10}C_3$

                                                                           =$\frac{15!}{1!(15-1)!} \times \frac{10!}{3!(10-3)!}$

                                                                           =$1800$

Now Committee with 4 girls

No. of ways = $^{10}C_4$

                    = $\frac{10!}{4!(10-4)!}$

                    = $210$

So, the committee consists at least three girls can be formed in no. of ways = 1800+210=2010

Hence there are 2010 ways to form the committee consists at least three girls