# CAT 1996 | Question: 143

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A man has nine friends, four boys and five girls. In how many ways can he invite them, if there have to be exactly three girls in the invitees?

1. $320$
2. $150$
3. $80$
4. $200$

No. Of combinations girls can be invited: 5C3 = 10

Now there are 5 possibilities.

1: no boy is invited: 4C0 =1 , combining it with combinations of girls 1 * 10 = 10

2: 1 boy is invited: 4C1 = 4, combining it with combinations of girls 4 * 10 = 40

3: 2 boys were invited: 4C2 = 6, 6 * 10= 60

4: 3 boys were invited : 4C3 = 4, 4 * 10 = 40

5: all boys were invited: 4C4 = 1, 1 * 10 = 10

So, total no of ways of inviting 3 girls = 10 + 40 + 60 + 40 + 10 = 160

So ,  Correct Answer is 160.

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