Question

15.A committee of 8 students is to be formed out of 5 boys and 8 girls. In how
many ways can it be done so that the number of girls is not less than the
number of boys?​

Answer 1

Answer:

5boys and 8girls.....

Step-by-step explanation:

1)5girls 3boys

2)6girls 2boys

3)7girls 1boy

4)4girls 4boys

Answer 2

Answer:

In this question, we have to find possible ways in which the number of selected girls should be no less than selected number of boys.

Step-by-step explanation:

Given: Total no. of girls from which the students have to be selected = 8

           Total no. of boys from which the students have to be selected = 5

To Find: no. of possible ways to select 8 students so that girls would be no less than boys.

Now, we have to apply combination here because we have to only do selection and order of selection don't basically matters. Hence,

For no. of girls to be more than boys, we can select one boy from 5 and 7 girls from 8 for the first case.

Therefore, First outcome = ⁵C₁ × ⁸C₇

This is the first way. Similarly, we can select 2 boys for 6 girls, 3 boys for 7 girls and 4 boys for 4 girls. We cannot proceed further as then no. of girls would be less than boys which is restricted. Therefore,

Possible ways would be = ⁵C₁ × ⁸C₇ + ⁵C₂ × ⁸C₆ + ⁵C₃ × ⁸C₇ + ⁵C₄ × ⁸C₄