JEE PYQ: Permutation And Combination Question 48
Question 48 - 2019 (12 Jan Shift 2)
Consider three boxes, each containing 10 balls labelled 1, 2, …, 10. Suppose one ball is randomly drawn from each of the boxes. Denote by $n_i$, the label of the ball drawn from the $i^{\text{th}}$ box, ($i = 1, 2, 3$). Then, the number of ways in which the balls can be chosen such that $n_1 < n_2 < n_3$ is:
(1) 120
(2) 82
(3) 240
(4) 164
Show Answer
Answer: (1)
Solution
Choose 3 distinct numbers from 10: ${}^{10}C_3 = 120$. Each selection gives exactly one arrangement with $n_1 < n_2 < n_3$. So answer $= 120$.
BETA
