10 t-shirts are available to choose. 5 of them are printed, and 5 of them are plain t-shirts. If 3 t-shirts are to be selected at random from the 10, what is the probability that at least one of them is a printed t-shirt. Options.
A) 1/12
B) 7/12
C) 5/12
D) 11/12
E) 13/12
You have 10 t-shirts. You need to choose 3 of them. You can do this in 10C3 = 10*9*8/3*2*1 = 120 ways.   You have 5 plain t-shirts. You can choose 3 out of them in 5C3 = 5*4/2= 
<gadget id="calculator">5*4/2</gadget>
<output>10</output>
10 ways.   So you have total 120 ways of picking 3 t-shirts out of 10. In 10 of those ways, you pick all plain t-shirts. So what happens in the rest of the 110 ways? In those, you must be picking up at least one printed t-shirt.   So probability of picking at least one printed t-shirt= 110/120 = 11/12   Answer is 11/12
<result>D</result>
10 t-shirts are available to choose. 5 of them are printed, and 5 of them are plain t-shirts. If 3 t-shirts are to be selected at random from the 10, what is the probability that at least one of them is a printed t-shirt.