Question

Each of four friends orders a sweatshirt from a catalog. There are 14 colors of sweatshirts, 7 of which are all cotton and 7 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?

Answer 1

The best way to solve this equation is to multiply the probability of them each getting a cotton sweater. The first fraction would be 1/2 because half of the sweaters are cotton at this point. The second one would be 6/13 because there are now six cotton sweaters out of the thirteen sweaters left. The third would be 5/12 because there are now five cotton sweaters out of the twelve sweaters left. The last one would be 4/11 because there are now four cotton sweaters out of the eleven sweaters left. you would then multiply 2 by 13 getting 26, then multiply 26 by 12 getting 312. Finally, multiply 312 by 11 getting 3,432, which would be your denominator. You would then multiply 6, 5, and 4 getting 120, your numerator. Getting your simplified answer 5/143.