A bag contains 3 white marbles and 3 black marbles. If each of 3 girls and 3 boys randomly selects and keeps a marble, what is the probability that all of the girls select the same colored marble?
Choose the correct choice from the following answers:
A) 1/35
B) 1/10
C) 1/15
D) 1/20
E) 1/25
first, total ways to select for all boys and girls, i.e 6!/(3!*3!) = 6*5*4*3*2*1/3*2*1*3*2*1=20   then there are one two way girls can have all same colors, either white or black.   The number of ways in which 3 girls can select 3 white balls = 3C3 = 1   The number of ways in which 3 girls can select 3 black balls = 3C3 = 1   Therefore, total favorable outcomes/total outcomes = 2/20= 1/10   1/10
<result>B</result>
A bag contains 3 white marbles and 3 black marbles. If each of 3 girls and 3 boys randomly selects and keeps a marble, what is the probability that all of the girls select the same colored marble?