Assume that there are 6 different issues of Time magazine, 7 different issues of Popular Science, and 3 different issues of Sports Illustrated, including the December 1st issue, on a rack.

Question

You choose 4 of them at random.

(1.)What is the probability that you choose 3 issues of Time and 1 issue of Popular Science? 

(2) What is the probability that you choose at least 1 of the Popular Science magazines? 

Answer 1

The denominator is D = (16 choose 4) = 16*15*14*13 / (4*3*2*1) =

4*5*7*13 <-- 16 cancels 4, 15 cancels 3, 14 cancels 2

140*13 =

1820

(1) (6 choose 3)(7 choose 1) / 1820 =

(6*5*4/(3*2)) (7) / 1820 =

140/1820 =

70/910

= 1/13

(2) Prob ( at least one popular science) = 1 - Prob( NO popular science)

= Prob(No popular science) = (13 choose 4) / 1820

= 13*12*11*10 / (4*3*2*1) over 1820

= (13*11*5)/1820

= (13 * 55)/1820

= (10+3)*55 over 1820

= (550 + 165) over 1820

= 715/1820

= 143/364