A team of 10 is to be formed from 4 girls and 11 boys. How many ways this can be

Question

A team of 10 is to be formed from 4 girls and 11 boys. How many ways this can be done by taking at most 3 girls in the team?

Answer: Option B
:
B
Case 1- No girls
Possible selections =

^{11} C_{10} = 11

Case 2- One girl
Possible selections=

4 \times^{11} C_{9} = 220

Case 3- Two girls
Possible selections =

^{4} C_{2} \times^{11} C_{8} = 990

Case 4- Three girls
Possible selections =

^{4} C_{3} \times^{11} C_{7} = 1320

Total= 2541

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