Question

Out of 6 boys and 4 girls, a group of 7 is to be formed. In how many ways can this be done if the group is to have a majority of boys?

• A. 120
• B. 90
• C. 100
• D. 80

Answer 1

The correct option is C

100

Form different cases in which boys are in majority compare to girls.
Case1: 1 girl and 6 boys, No. of ways they can be selected =${}^4{C}_1\times {}^6{C}_6=4$

Case2: 2 girls and 5 boys, No. of ways they can be selected = ${}^4{C}_2\times {}^6{C}_5=36$

Case3: 3 girls and 4 boys, No. of ways they can be selected = ${}^4{C}_3\times {}^6{C}_4=60$

Hence total ways $60-36+4=100$ .