Cybil and Ronda are sisters. The 10 letters from their names are placed on identical cards so that each of 10 cards contains one letter. Without replacement, two cards are selected at random from the 10 cards. What is the probability that one letter is from each sister's name? Express your answer as a common fraction
We can count sets here.....
No. of possible sets = C(10,2) = 45
No. of sets containing only letters from Cybil's name = C(5,2) = 10
No. of sets containing only letters from Ronda's name = C(5,2) = 10
So the number of sets containing one letter from each name = 45 - 10 - 10 = 25
So....the probability of choosing one of these sets = 25 / 45 = 5 / 9