I have a drawer with 4 shirts, 5 pairs of shorts, and 6 pairs of socks in it. If I reach in and randomly remove three articles of clothing, what is the probability that I get one shirt, one pair of shorts, and one pair of socks? (Treat pairs of socks as one article of clothing.)
+33666 Prob of shirt followed by shorts followed by socks = (4/15)*(5/14)*(6/13) = (4*5*6)/(15*14*13)
Prob of shirt followed by socks followed by shorts = (4/15)*(6/14)*(5/13) = (4*5*6)/(15*14*13)
Prob of shorts followed by shirt followed by socks = (5/15)*(4/14)*(6/13) = (4*5*6)/(15*14*13)
... etc. 3! possibilities
So probability = 3!*(4*5*6)/(15*14*13) = 24/91 ≈ 0.264
.
+33666 Prob of shirt followed by shorts followed by socks = (4/15)*(5/14)*(6/13) = (4*5*6)/(15*14*13)
Prob of shirt followed by socks followed by shorts = (4/15)*(6/14)*(5/13) = (4*5*6)/(15*14*13)
Prob of shorts followed by shirt followed by socks = (5/15)*(4/14)*(6/13) = (4*5*6)/(15*14*13)
... etc. 3! possibilities
So probability = 3!*(4*5*6)/(15*14*13) = 24/91 ≈ 0.264
.
