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Question

A bag contains 30 tokens numbered serially from 0 to 29. The number of ways of selecting 3 tokens from the bag, such that sum of numbers on them is 30, is

A
56
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B
75
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C
90
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D
105
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Solution

The correct option is B 75
Here, order of selection won't matter
one of the coin other two coins No. of ways
0 (1,29).....(14,16) 14
1 (2,27).....(14,15) 13
2 (3,25).....(13,15) 11
3 (4,23).....(13,14) 10
4 (5,21).....(12,14) 8
5 (6,19)....(12,13) 7
6 (7,17)...(11,13) 5
7 (8,15)..(11,12) 4
8 (9,13)(10,12) 2
9 (10,11) 1

Hence, required number of ways =14+13+11+10+8+7+5+4+2+1=75

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