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Mathematics Question on Probability

A bag contains n coupons marked 1, 2, 3, ........ n. If two coupons are drawn then the chance that the difference of the coupons exceeds m (less than n -1) is:

A

(n−m)(n−m−1)n(n−1)\frac {(n-m)(n-m-1)} {n(n-1)}

B

(n−m)(n+m−1)n(n−1)\frac {(n-m)(n+m-1)} {n(n-1)}

C

(n+m)(n+m−1)n(n−1)\frac {(n+m)(n+m-1)} {n(n-1)}

D

none of these

Answer

(n−m)(n−m−1)n(n−1)\frac {(n-m)(n-m-1)} {n(n-1)}

Explanation

Solution

Answer (a) (n−m)(n−m−1)n(n−1)\frac {(n-m)(n-m-1)} {n(n-1)}