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Q.

Out of 7 men and 4 women a committee of 5 is to be formed. The number of ways  in which this can be done 
    I. So as to include exactly 2 women is 210.
    II. So as to include at least 2 women is 301.
Which of the above statements is true? 

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a

Only I          

b

Only II          

c

Both I and II          

d

Neither I nor II

answer is C.

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Detailed Solution

I.   7C3×4C2=210⇒true

II.  7C3×4C2+7C2×4C3+7C1×4C4=301⇒true

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