Q6
Consider three boxes, each containing 10 balls labelled
1,2.., 10. Suppose one ball is randomly drawn from each of
the boxes. Denote by ni, 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 n1 <n2 <n3 is:
(1) 120
(2) 82
(3) 240
(4) 164
Answers
Given : three boxes, each containing 10 balls labelled 1,2.., 10.
To find : the number of ways in which the balls can be chosen such that n1 <n2 <n3 is:
Solution:
Box 1 Box 2 Box
1 2 3 - 10 ( 8 ways)
3 4 - 10 ( 7 ways)
---.......
9 10 ( 1 way)
Number of ways = 8 + 7 + ---------+ 2 + 1
= 36
Box 1 Box 2 Box
2 3 4 - 10 (7 ways)
4 5 - 10 ( 6 ways)
---.......
9 10 ( 1 way)
Number of ways = 7 + ---------+ 2 + 1
= 28
Box 1 Box 2 Box
3 4 5 - 10 (6 ways)
5 6 - 10 ( 5 ways)
---.......
9 10 ( 1 way)
Number of ways = 6 + ---------+ 2 + 1
= 21
and so on
Total ways =
36 + 28 + 21 + 15 + 10 + 6 + 3 + 1
= 120
120 Ways in which the balls can be chosen such that n1 <n2 <n3
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