Question

there are 15 boys snd 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

committee with at least three girl =( committee with 3 girl + committee with 4 girl )
committee with 3 girl =(15C1)×(10C3) = 15×120 = 1800
committee with 4 girl = (10C4) = 210
so the required number of ways = 1800 +210 = 2010

Answer 2

Answer:

There are 2010 No. of ways of forming a four member committee with at least 3 girls

Step-by-step explanation:

Given : No. of boys = 15

             No. of girls = 10

To Find :No. of ways of forming a four member committee with at least 3 girls

Solution:

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

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 No. of ways of forming a four member committee with at least 3 girls