Description for Correct answer:
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 \( \Large ^{4}C_{2} \times ^{5}C_{3} \) ways. '

ll. Selecting, 3 girls out of 4 and 3 boys out of 5. This can be done in \( \Large ^{4}C_{3} \times ^{5}C_{2} \) ways.

III. Selecting 4 girls out of 4 and 1 boy out of 5. This can be done in \( \Large ^{4}C_{4} \times ^{5}C_{1} \) 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.

\( \Large ^{4}C_{3} \times ^{5}C_{3} \)

=\( \Large ^{4}C_{2} \times ^{5}C_{3} + ^{4}C_{3} \times ^{5}C_{2} + ^{4}C_{4} \times ^{5}C_{1} \)

=\( \Large \frac{4 \times 3}{1 \times 2} \times \frac{5 \times 4 \times 3}{1 \times 2 \times 3} + \frac{4 \times 3 \times 2}{1 \times 2 \times 3} \times \frac{5 \times 4}{1 \times 2} + 1 \times 5 \)

= 60 + 40 + 5 = 105