JEE Main 2023 · 8 April · morning · Single correct · +4 / −1

Let the number of elements in sets A and B be five and two respectively. Then the number of subsets of A × B each having at least 3 and at most 6 elements is :

  1. (a) 782
  2. (b) 772
  3. (c) 752
  4. (d) 792
Answer and solution

Answer (d) 792

Solution

Maths sir · 3 steps

Find how many pairs A × B has, then add the ways to pick 3, 4, 5 or 6 of them.

  1. Count the pairs. Each of the 5 elements of A pairs with each of the 2 elements of B. So n(A × B) = 5 × 2 = 10.
  2. Count by size. A subset with exactly r elements is a choice of r pairs out of 10, so there are C(10, r) of them. We need r = 3, 4, 5, 6.

    C(10, 3)+C(10, 4)+C(10, 5)+C(10, 6) = 120 + 210 + 252 + 210

  3. So. The total is 120 + 210 + 252 + 210 = 792, which is option (d).

The idea to keep. To count subsets of a given size, first find how many elements the set has, then use C(n, r). For A × B, the number of elements is n(A) × n(B).

Answer from the NTA final answer key. Solution by PrepWiser.

Study Sets

Asked about 40 times in JEE Main since 2020. This question is from 2023.