IIT JEE 1982 Maths - MCQ Question 1
Eight chairs are numbered 1 to 8. Two women and three men wish to occupy one chair each. First the women choose the chairs from amongst the chairs marked 1 to 4; and then the men select the chairs from amongst the remaining. The number of possible arrangements is
Note C(n, r) and P(n, r) denote the combination and permutations of r objects out of n, respectively.
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1 solution
2 women can choose and arrange themselves on the first four chairs in P(4, 2) ways (since the chairs are numbered or arranged, they are distinct). 3 men can choose and arrange themselves in the remaining 6 chairs in P(6, 3) ways. Hence, the required number of ways is P(4, 2)*P(6, 3), which is 'None of the others'.