Question

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

• A. 105
• B. 60
• C. 100
• D. 120
• E. None of these

Answer 1

The correct option is A 105

A team of 5 children, consisting of atleast 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 ${}^4{C}_3\times {}^5{C}_3$ ways.
II. Selecting 3 girls out of 4 and 2 boys out of 5. This can be done in ${}^4{C}_3\times {}^5{C}_2$ ways.
Ill. Selecting 4 girls out of 4 and 1 boy out of 5. This can be done in ${}^4{C}_4\times {}^5{C}_1$ 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
$={}^4{C}_2\times {}^5{C}_3+{}^4{C}_3\times {}^5{C}_2+{}^4{C}_4\times {}^5{C}_1=\frac{4\times 3}{1\times 2}\times \frac{5\times 4\times 3}{1\times 2\times 3}+\frac{4\times 3\times 2}{1\times 2\times 3}\times \frac{5\times 4}{1\times 2}+1\times 5$
= 60 + 40 + 5 = 105