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1

IIT-JEE 1994

Subjective
A committee of 12 is to be formed from 9 women and 8 men. In how many ways this can be done if at least five women have to included in a committee? In how many of these committees? In how may of these committees
(a) The women are in majority?
(b) The men are in majority?

Answer

6072, (a) 2702, (b) 1008
2

IIT-JEE 1991

Subjective
Eighteen guests have to be seated, half on each side of a long table. Four particular guests desire to sit on one particular side and three others on the other side. Determine the number of ways in which the sitting arrangements can be made.

Answer

$${}^{11}{C_5} \times 9\,!\, \times \,9\,!$$
3

IIT-JEE 1986

Subjective
A box contains two white balls, three black balls and four red balls. In how many ways can three balls be drawn from the box if at least one black ball is to be included in the draw?

Answer

64
4

IIT-JEE 1985

Subjective
7 relatives of a man comprises 4 ladies and 3 gentlemen ; his wife has also 7 relatives ; 3 of them are ladies and 4 gentlemen. In how many ways can they invite a dinner party of 3 ladies and 3 gentlemen so that there are 3 of man's relatives and 3 of the wife's relatives?

Answer

485

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Class 12