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Question

# The number of combinations of 2n things taken n at a time when n of the 2n things are alike and the rest different is

A
2nC0+2nC1+2nC2+.....+2nCn
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B
(2n)!n!
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C
(2n)!(n!)2
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D
2n
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Solution

## The correct option is C 2nWe have n things which are alike and n different things, making a total of 2n things.At a time, we want to take n things, and so the options would be 0 from the first set n from the second set, 1 from the first set (n−1) from the second set and so on.So the number of combinations would be nC0×1+nC1×1+nC2×1+....+nCn×1 since the number of combinations of picking up alike objects is only 1 in all the cases.The expression sums up to 2n

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