Question

I get 2/7 for the answer but the text says it's 4/7 and I don't understand why. Tim hung up a red shirt, 2 blue shirts and 2 white shirts and also a black pair of pants and a blue pair. 2 fell off the hangers. What's the probability that the red shirt and black pants fell on the floor?

Answer 1

I get a different answer altogether.
P(red shirt fell 1st) = 1/7, P(black pants fell next) = 1/6
so P(red shirt fell 1st and then black pants) = 1/7 * 1/6 = 1/42
similarly, P(black pants fell 1st then red shirt) = 1/42
so, P(red shirt and black pants fell) = 1/42 + 1/42 = 2/42 = 1/21

Answer 2

asnaseer's idea seems fine .. this is actually elementary mutual inclusion exclusion.