UGC NET CSE | December 2015 | Part 2 | Question: 1

Question

How many committees of five people can be chosen from 20 men and 12 women such that each committee contains at least three women

• A. 75240
• B. 52492
• C. 41800
• D. 9900

Answer 1

Total 5 people need to be chosen with condition that at least 3 must be women and no restriction on men

For that, we have 20 men and 12 women 

Case 1: Take 2 men from 20 men and 3 women from 12 women

               ²⁰C₂  * ¹²C₃

Case 2: Take 1 man from 20 men and 4 women from 12 women

                  ²⁰C₁ * ¹²C₄

Case 3: Take 0 man from 20 men and 5 women from 12 women

                 ²⁰C₀ * ¹²C₅

All these 3 cases are mutually exclusive:

ANS= ²⁰C₂  * ¹²C₃  +  ²⁰C₁ * ¹²C₄  +  ²⁰C₀ * ¹²C5

ANS=52492

Comments

Can u plz explain what is C???

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c means combination.

nCr=n!/(n-r)!.r!

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Are there any shortcuts? this is a tedious way of doing it.