probability confusion

[bennachie]

Going through a practice paper I came across this question.

A building has 20 floors

4 floors have shops only
9 floors are offices only
7 floors are apartments only

3 floors are chosen at random for safety checks

what is the probability that:

a) All three floors have apartments
b) Two floors have shops and one floor has offices
c) The floors are of different types

My workings
for a) p = 7/20 x 6/19 x 5/18
for b) p = 4/20 x 3/19 x 9/18
for c) p = 4/20 x 9/19 x 7/18

Seems like a is right but the other two are wrong, just wondering why.

 

[MarkFL]

Hello, and welcome to FMH!

For b), you have found the probability that "Two floors have shops and one floor has offices" but you are restricting yourself to just one arrangement. How many different ways can we arrange 2 floors with shops and one floor with offices?

 

[Steven G]

Think hypergeometric