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Consider three boxes, each containing 10...

Consider three boxes, each containing 10 balls labelled 1, 2, …, 10. Suppose one ball is randomly drawn from each of the boxes denoted by `n_(i)`, the label of the ball drawn from the `i^(th)` 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

Text Solution

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The correct Answer is:
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.`
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