A family has seven children. Assume each of the children is equally likely to be either a boy or a girl.

**1 )** If the children are listed in the order of birth (Example: B,B,G,B,G,G,B)

How many such listings are possible?

**2 )** What is the probability that the family has exactly two girls?

**1 )** 128 Listing possibilities.

For each place in the order we have 2 chances (either boy or girl)

2x2x2x2x2x2x2 = 128 possibilities

**2 )** 21 Combinations possibile for exact 2 girls.Lets take each scenario

Suppose first child is a Girl, So we have 6 possibilities in this case to have exactly 2 girls

G,X,X,X,X,X,X - Any of the 'X' can be a Girl child and we have 6 possibilities for that

G,G,X,X,X,X,X

G,X,G,X,X,X,X

G,X,X,G,X,X,X

G,X,X,X,G,X,X

G,X,X,X,X,G,X

G,X,X,X,X,X,G

Now we can take the case when second child is Girl: We have 5 possibilties

(Note first child will be a Boy in this case as we have considered first child- Girl possibiliry already

B,G,G,X,X,X,X

B,G,X,G,X,X,X

B,G,X,X,G,X,X

B,G,X,X,X,G,X

B,G,X,X,X,X,G

Possibilities when Third child is Girl: We have 4 possibilties

B,B,G,G,X,X,X

B,B,G,X,G,X,X

B,B,G,X,X,G,X

B,B,G,X,X,X,G

Possibilities when fourth child is Girl: We have 3 possibilties

B,B,B,G,G,X,X

B,B,B,G,X,G,X

B,B,B,G,X,X,G

Possibilities when Fifth child is Girl: We have 2 possibilties

B,B,B,B,G,G,X

B,B,B,B,G,X,G

Possibilities when Sixth child is Girl: We have only 1 possibilty

B,B,B,B,B,G,G

In short : 6+5+4+3+2+1 = 21

There is no comments