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JEE Main 2019 · 12 Jan · Shift I

JEE Main 2019 Mathematics question on Permutations and Combinations

Consider three boxes, each containing 10 balls labelled 1, 2, ..., 10. Suppose one ball is randomly drawn from each of the boxes. Denote by nin_i, the label of the ball drawn from the iith box, (i=1,2,3)(i = 1, 2, 3). Then, the number of ways in which the balls can be chosen such that n1<n2<n3n_1 < n_2 < n_3 is
  1. A.
    82
  2. B.
    120
  3. C.
    240
  4. D.
    164
Show answer and solution

Correct option: B

Solution

The number of ways to choose 3 distinct values from {1,...,10} and arrange them in strictly increasing order is C(10,3) = 120. Each such combination corresponds to exactly one ordered triple (n₁, n₂, n₃) with n₁ < n₂ < n₃, since the increasing assignment is unique. Hence the answer is 120.

[JEE Main 2019 · 12 Jan · Shift I]

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