Assume that there are 7 different issues of Newsweek, 8 different issues of Time, and 4 different issues of Sports Illustrated, including the December 1st issue, on the rack. You choose 4 of them at random.
(1) What is the probability that you choose 2 issues of Newsweek and 2 issues of Time?
To calculate the probability of choosing 2 issues of Newsweek and 2 issues of Time, we need to first determine the total number of possible outcomes.
Total number of possible outcomes = Total number of ways to choose 4 issues from the available pool of 19 issues (7 Newsweek + 8 Time + 4 Sports Illustrated)
We can calculate the total number of possible outcomes using the combination formula:
nCr = n! / (r!(n-r)!)
In this case, n = 19 (total number of available issues) and r = 4 (number of issues to choose).
Total number of possible outcomes = 19! / (4!(19-4)!) = 19! / (4!15!) = (19 * 18 * 17 * 16) / (4 * 3 * 2 * 1) = 4845
Next, we need to determine the number of favorable outcomes, which is the number of ways to choose 2 Newsweek issues and 2 Time issues.
Number of favorable outcomes = (Number of ways to choose 2 issues from 7 Newsweek) * (Number of ways to choose 2 issues from 8 Time)
= 7C2 * 8C2
= (7! / (2!(7-2)!)) * (8! / (2!(8-2)!))
= (7! / (2!5!)) * (8! / (2!6!))
= (7 * 6 / (2 * 1)) * (8 * 7 / (2 * 1))
= (21) * (28)
= 588
Finally, we can calculate the probability.
Probability = Number of favorable outcomes / Total number of possible outcomes
= 588 / 4845
≈ 0.1214 or 12.14% (rounded to 2 decimal places)
Therefore, the probability of choosing 2 issues of Newsweek and 2 issues of Time from the given pool is approximately 0.1214 or 12.14%.