A team of 5 children is to be selected out of 4 girls and 5 boys such that it contains at least 2 girls. In how many different ways the selection can be made?

Explanation:

A team of 5 children consisting of at least two girls can be formed in following ways:

I. Selecting 2 girls out of 4 and 3 boys out of 5. This can be done in ^4C2×^5C3 ways. ‘

ll. Selecting, 3 girls out of 4 and 3 boys out of 5. This can be done in ^4C3×^5C2 ways.

III. Selecting 4 girls out of 4 and 1 boy out of 5. This can be done in ^4C4×^ 5C1 ways.

Since the team is formed in each case, therefore, by the fundamental principle of addition, the total number of ways of forming the team.

4C3×5C3

=4C2×5C3+4C3×5C2+4C4×5C1

=4×3\1×2 × 5×4×3\1×2×3 + 4×3×2\1×2×3 × 5×4\1×2 + 1×5

= 60 + 40 + 5 = 105