Q. 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) 80
C) 90
D) 100
Explanation
(d)
The boys are in majority, if the groups are 4B, 3G, 5B, 2G, 6B 1G
Total number of combinations
$= \ ^{6}C_{4} \times \ ^{4}C_{3} + \ ^{6}C_{5} \times \ ^{4}C_{2} + \ ^{6}C_{6} \times \ ^{4}C_{1}$
$= 15 \times 4 + 6 \times 6 + 1 \times 4 = 100$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.