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?

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.