Question

In a group of 6 boys and 4 girls, four children are to be selected. In how many different ways can they be selected such that at least one boy should be there?​

Answer 1

Answer:

As the question asks about at least one boy should be selected, so from total no. of ways of selecting 4 children subtract none of the boys which gives us one boys + 2 boys + 3 boys + 4 boys, which is our required answer at least one boys. So the answer is C(10,4)-C(4,4)=209. C(10,4) is no. of ways of selecting 4 children's from 6 boys and 4 girls. C(4,4) is no. of ways of selecting 4 girls from 4 girls which is 1 way. So the answer is 209.

                                                                or

In the second method let’s select 1 boy, 3 girls + 2 boys, 2 girls + 3 boys, 1 girl + 4 boys which is C(6,1)*C(4,3) + C(6,2)* C(4,2) + C(6,3)* C(4,1)+ C(6,4)= 209. In both ways answer is 209.

Step-by-step explanation:

Answer 2

We may have (1 boy and 3 girls) or (2 boys and 2 girls) or (3 boys and 1 girl) or (4 boys).

Required number

of ways = (6C1 x 4C3) + (6C2 x 4C2) + (6C3 x 4C1) + (6C4)

= (6C1 x 4C1) + (6C2 x 4C2) + (6C3 x 4C1) + (6C2)

= (6 x 4) + 6 x 5 x 4 x 3 + 6 x 5 x 4 x 4 + 6 x 5

2 x 1 2 x 1 3 x 2 x 1 2 x 1

= (24 + 90 + 80 + 15)

= 209.