Permutations and Combinations 3 Question 3
3. Consider three boxes, each containing 10 balls labelled $1,2, \ldots, 10$. Suppose one ball is randomly drawn from each of the boxes. Denote by $n _i$, the label of the ball drawn from the $i$ 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
(2019 Main, 12 Jan I)
(a) 82
(b) 120
(c) 240
(d) 164
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Answer:
Correct Answer: 3. (b)
Solution:
- 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 $i$ 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 same as selection of 3 different numbers from numbers ${1,2,3, \ldots, 10}={ }^{10} C _3$ $=120$.
