from a group of 7 boys and 3 girls a committee of 4 person is to be formed so as to include 2boys and 2 girls in how many ways can the committee form
Answers
Answer:
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Step-by-step explanation:
To answer this determine the different manners in which it can happen and for each different manner how many ways that manner can occur. Then add them up.
A: A group of 6 containing 4 girls and 2 boys. 4C4 is the way to choose 4 girls from 4 girls. --- 7C2 is the way to choose 2 boys from 7 boys. -- So 4C4 x 7C2 = 1 x 21 = 21
B: A group of 6 containg 3 girls and 3 boys. ---- 4C3 x 7C3 = 4 x 35 = 140
C: A group containing 2 girls and 4 boys. --- 4C2 x 7C4 = 6 x 35 = 210.
21 + 140 + 210 = 371.
As a check, determine the total number of ways to choose 6 people from 11. Which is 11C6 = 462. And then subtract out the number of groups which have no girls which is 4C0 × 7C6 = 1 x 7 = 7. And also subtract out the number of groups which have only 1 girl which is 4C1 x 7C5 = 4 x 21 = 84.
462 - 7 - 84 = 371.
It's nice to have a corroboration of your method because counting problems are slippery. It's easy to make a logic or computational error. Here's hoping I haven't made one.