# 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?

May 3, 2017

There are $7 {C}_{3}$ ways of choosing 3 cards from the deck. That's the total number of outcomes.

If you end up with the 2 unmarked and 1 marked card:

• there are $5 {C}_{2}$ ways of choosing 2 unmarked cards from the 5, and

• $2 {C}_{1}$ ways of choosing 1 marked cards from the 2.

So the probability is:

$\frac{5 {C}_{2} \cdot 2 {C}_{1}}{7 {C}_{3}} = \frac{4}{7}$