Probability Word Problem

Question

Leo has 8 buttons, 5 of which are red. If Leo randomly picks 4 buttons, what is the probability that all of them are red?

Answer 1

For 5 red buttons, we multiply the fraction (5/8) for the first pick. (4/7) for the second pick. (3/6) for the third. (2/5) for the fourth. (1/4) for the fifth. Our equation: (5/8)*(4/7)*(3/6)*(2/5)*(1/4)= 120/6720

Answer 2

Picking the first one, you have a probability of 5/8. Now there are only 4 red left out of 7, or 4/7. Then there are 3 out of 6 or 3/6 and so on until you have all 5 red buttons.

(5/8)(4/7)(3/6)(2/5)(1/4) = 120/6720

Notice that this is also equal to 5•4•3•2•1/(8•7•6•5•4) = 5!/(8!/3!)