Three cards are selected at random from a group of 7. Two of the cards have been marked with winning numbers. What is the probability that exactly 1 of the 3 cards has a winning number?
If you end up with the 2 unmarked and 1 marked card:
#5C_2#ways of choosing 2 unmarked cards from the 5, and
#2C_1#ways of choosing 1 marked cards from the 2.
So the probability is: