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.

What is the probability that you choose at least 1 of the Time magazines?

With no restriction, number of ways to choose 4

- C(19.4) = 3876

number of ways to choose 4 with NO Time magazines
= C(11,4) = 330

so the number of ways with at least one Time = 3876-330 = 3546

prob(at least one Time) = 3546/3876 = 591/646 or appr .915

thank you so much! i appreciate you writing out how to solve it rather than just giving me an answer by itself....def helped me understand

To calculate the probability of choosing at least 1 of the Time magazines, we need to find the probability of not choosing any Time magazines and subtract it from 1.

The total number of possible outcomes is the number of ways to choose any 4 magazines out of the total available, which is given by the combination formula:

Total possible outcomes = C(7+8+4, 4) = C(19, 4) = (19!)/(4!(19-4)!) = (19!)/(4!15!) = (19*18*17*16)/(4*3*2*1) = 38,760

Now, let's calculate the number of outcomes where no Time magazine is chosen. To have no Time magazines, we can choose any 4 magazines out of the remaining 7 from Newsweek and 4 from Sports Illustrated:

Outcomes without Time magazines = C(7+4, 4) * C(4, 4) = C(11, 4) * C(4, 4) = (11!)/(4!(11-4)!) * (4!)/(4!(4-4)!) = (11*10*9*8)/(4*3*2*1) * 1 = 330

Therefore, the probability of not choosing any Time magazines is:

P(No Time) = Outcomes without Time magazines / Total possible outcomes = 330 / 38,760 = 0.008509

Finally, the probability of choosing at least 1 of the Time magazines is:

P(At least 1 Time) = 1 - P(No Time) = 1 - 0.008509 = 0.991491

So, the probability of choosing at least 1 of the Time magazines is approximately 0.991491, or about 99.15%.

To find the probability of choosing at least 1 Time magazine, we need to consider the total number of possible outcomes (sample space) and the number of desired outcomes (favorable outcomes). Here's how we can calculate it step by step:

Step 1: Calculate the total number of possible outcomes.
Since we are choosing 4 magazines from a selection of 7 Newsweek, 8 Time, and 4 Sports Illustrated, the total number of possible outcomes is the combination of the three categories: 7 + 8 + 4 = 19 different magazines.

Step 2: Calculate the number of desired outcomes.
To find the number of desired outcomes, we need to consider the cases where we choose at least 1 of the Time magazines. This means we can either choose 1, 2, 3, or 4 Time magazines. Let's calculate the number of possibilities for each case:

- Choosing 1 Time magazine: There are 8 options for choosing 1 Time magazine, and the remaining 3 magazines can be chosen from the remaining 19 - 1 = 18 options. Therefore, the number of possibilities for this case is 8 * 18C3.
- Choosing 2 Time magazines: There are 8C2 options for choosing 2 Time magazines, and the remaining 2 magazines can be chosen from the remaining 19 - 2 = 17 options. Therefore, the number of possibilities for this case is 8C2 * 17C2.
- Choosing 3 Time magazines: There are 8C3 options for choosing 3 Time magazines, and the remaining 1 magazine can be chosen from the remaining 19 - 3 = 16 options. Therefore, the number of possibilities for this case is 8C3 * 16C1.
- Choosing 4 Time magazines: There is only 1 option for choosing all 4 Time magazines, and no magazines are left to choose from the remaining 19 - 4 = 15 options.

Step 3: Calculate the probability of choosing at least 1 Time magazine.
Finally, we can calculate the probability by summing up the number of desired outcomes and dividing it by the total number of possible outcomes.

Probability = (Number of desired outcomes) / (Total number of possible outcomes)
Probability = [8 * 18C3 + 8C2 * 17C2 + 8C3 * 16C1 + 1] / (19C4)

By plugging in the values and evaluating the expression, you can find the probability of choosing at least 1 of the Time magazines.