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Q.

If the difference of the number of arrangements of three things from a certain number of dissimilar things and the number of selections of the same number of things from them exceeds 100, then the least number of dissimilar things is

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a

8

b

6

c

5

d

7

answer is D.

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Detailed Solution

Here, nP3−nC3>100or  n!(n−3)!−n!3!(n−3)!>100or  56n(n−1)(n−2)>100or  n(n−1)(n−2)>120or  n(n−1)(n−2)>6×5×4or  n=7,8,…
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