A bag contains 6 white marbles and 6 black marbles. If each of 6 girls and 6 boys randomly selects and keeps a marble, what is the probability that all of the girls select the same colored marble?  Choose one.
A) 1/35 B) 1/10 C) 1/3 D) 1/462 E) 1/252
first, total ways to select for all boys and girls, i.e 12!/(6!*6!) = 12*11*10*9*8*7/6*5*4*3*2 =924   then there are one two way girls can have all same colors, either white or black.   The number of ways in which 6 girls can select 6 white balls = 6C6 = 1   The number of ways in which 6 girls can select 6 black balls = 6C6 = 1   Therefore, total favorable outcomes/total outcomes = 2/924 = 1/462   1/462
<result>D</result>
A bag contains 6 white marbles and 6 black marbles. If each of 6 girls and 6 boys randomly selects and keeps a marble, what is the probability that all of the girls select the same colored marble?