Each of four friends orders a sweatshirt from a catalog. There are 16 colors of sweatshirts, 7 of which are all cotton and 9 of which are a blend. Each one orders a different color (no repeats) at random. What is the probability that the friends order only cotton sweatshirts?
Since each friend orders a different color at random, the total number of ways they can order the sweatshirts is 16 * 15 * 14 * 13.
There are 7 cotton sweatshirts available and each friend must choose a cotton sweatshirt, so the number of ways they can all order cotton sweatshirts is 7 * 6 * 5 * 4.
Therefore, the probability that the friends order only cotton sweatshirts is:
(7 * 6 * 5 * 4) / (16 * 15 * 14 * 13) = 0.00752
So the probability is approximately 0.752%.
as a fraction
The probability of the friends ordering only cotton sweatshirts can be expressed as a fraction by simplifying the ratio of the number of ways they can order only cotton sweatshirts to the total number of ways they can order sweatshirts:
(7 * 6 * 5 * 4) / (16 * 15 * 14 * 13) = 840 / 43680
Therefore, the probability as a fraction is 840/43680, which can be further reduced by dividing both the numerator and denominator by 120:
840 ÷ 120 = 7
43680 ÷ 120 = 364
So, the probability as a simplified fraction is 7/364.
incorrect
Apologies for the oversight. Let's correct the calculation:
The probability of each friend ordering a cotton sweatshirt is 7/16. Since each friend is making an independent choice, the probability that all four friends order cotton sweatshirts is:
(7/16) * (6/15) * (5/14) * (4/13) = 840 / 43680
Which simplifies to:
840/43680 = 21/1092
Therefore, the probability that the friends order only cotton sweatshirts is 21/1092.
answer choices are 44/7 1/35 9/455 1/52
To find the probability that all four friends order cotton sweatshirts, we need to multiply the probabilities of each friend choosing a cotton sweatshirt.
For the first friend, the probability of selecting a cotton sweatshirt is 7 out of 16. For the second friend, the probability is 6 out of 15, for the third friend it is 5 out of 14, and for the fourth friend, it is 4 out of 13.
Therefore, the overall probability is:
(7/16) * (6/15) * (5/14) * (4/13)
= 840 / (16 * 15 * 14 * 13)
= 840 / 43680
= 21 / 1092
= 3 / 156
= 1 / 52
Therefore, the correct probability is 1/52.