Statitics and Probability PLEASE HELP

Question

There are 10 red, 5 blue and 3 green shirts in a drawer. A shirt is selected and then, without replacement,  the second shirt is selected. What is the probability that at least one red shirt will be selected?

Write your answer as a fraction,in the form a/b, for example 3/7. PLEASE reduce your fraction.

Answer 1

You are interested in the probability that the red shirt gets picked on the first or second try:

P(first try) = 10/18 [10 red/18 total shirts]

PLUS

P(second) = (8/18)*(10/17) [(8 non red/18 total)*(10 red/17 total remaining)]

This is equal to 1 minus the probability that a red shirt is never selected

P(never) = (8/18)*(7/17)