A drawer contains socks. When two socks are drawn at random, the
probability that both are red is 5/14. Which of the following can be
the number of socks in the drawer?  Choose the correct option.
A) 5  B) 6  C) 7  D) 8  E) 9
If there are n socks, r of which are red, in the drawer, then the probability that   two chosen together at random are red is   r/n *   r - 1/n - 1   =   5/14   Therefore, r(r - 1) = 5k and n(n- 1) = 14k for some positive integer k. Since 14 must   divide n(n - 1), the only choices given which need be considered are n = 7 and n = 8. If   n = 7, then n(n -1) = 14k implies k = 3 but then r(r - 1) = 5k = 15 is an impossibility.   If n = 8, we get k = 4 and r = 5, a valid possiblity. Therefore, the answer is n = 8.   correct answer 8
<result>D</result>
A drawer contains socks. When two socks are drawn at random, the
probability that both are red is 5/14. Which of the following can be
the number of socks in the drawer?