Question

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 ith box, (I = 1, 2, 3). Then, the number of ways in which the balls can be chosen such that `n_(1) lt n_(2) lt n_(3)` is
A. 82
B. 120
C. 240
D. 164

Answer 1

Correct Answer - B
Given there are three boxes, each containing 10 balls labelled 1, 2, 3, .. , 10.
Now, one ball is randomly drawn from each boxes, and `n_(i)` denote the label of the ball drawn from the ith box, (i = 1, 2, 3).
Then, the number of ways in which the balls can be chosen such that `n_(1) lt n_(2) lt n_(3)` is same as selection of 3 different numbers from numbers `{1, 2, 3, .. , 10} = ""^(10)C_(3) = 120.`