More Men
There are a total of men and women in a meeting and members are about to be elected randomly. The probability that the two elected are either both men or both women is . If there are more men than women, how many more men are in the meeting than women?
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Since the total number of persons is an odd number, one group has to be odd numbered and the other even numbered. The difference thus has to be odd. only 11 and 9 fit the bill. so the number of men has to be 36 or 35. Solving for 36C2+25C2 we see that it's 930 (multiple of 31), while the equivalent for 9 is 920. Thus the number of men is 36 and the difference is 11. Of course this works only for MCQs :-D