A classroom of children has 13 boys and 17 girls in which five students are chosen to do presentations. In how many ways can the five students be chosen so that more boys than girls are selected?

52,338

Explanation:

Since we have to choose such a group of 5 in which number of boys should be greater than the number of girls, therefore each group could have (3 boys, 2 girls) or (4 boys, 1 girl) or (5 boys, 0 girls).

Based on the above discussion the answer shall be:

Number of ways = 13C3 x 17C2+13C4 x 17C1+[13C5 x 17C0

=38,896+12,155+1,287

=52,338