JEE Main 12 Jan 2019 Morning Question 4
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 $ 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 [JEE Main Online Paper Held On 12-Jan-2019 Morning]
Options:
A) 120
B) 164
C) 240
D) 82
Show Answer
Answer:
Correct Answer: A
Solution:
- Let $ n _1=1, $ then $ n _2 $ can be 2, 3,…, 9 and $ n _3 $ can be 3,…., 10
$ \therefore $ No. of ways $ =8+7+6+5+4+3+2+1 $ $ =\frac{8\times 9}{2} $ Similarly, when $ n _1=2, $ then $ n _2 $ can be 3,…, 9 and $ n _3 $ can be 4,…., 10
$ \therefore $ No. of ways $ =7+6+5+4+3+2+1=\frac{7\times 8}{2} $ And so on.
$ \therefore $ Total required ways $ =\frac{8\times 9}{2}+\frac{7\times 8}{2}+….+\frac{2\times 3}{2}+\frac{1\times 2}{2}=\frac{240}{2}=120 $
