Maria and Thomas are part of a group of 12 women and 4 men w

Maria and Thomas are part of a group of 12 women and 4 men who will participate in a chess tournament. The 16 players will be randomly paired up into groups of two.

(c) What is the probability that Maria will be paired with another woman and Thomas will be paired with another with a man?


(d) What is the probability that both Maria and Thomas are paired with a woman?

A ski club with 5 members uses a similar storage system as the one described above. Each member normally hangs his (or her) ski poles on a hook, with each member using a separate hook. Suppose that the cleaning person takes down all the poles to wash the wall, and puts them back up randomly with two poles to each of the 5 hooks. What is the probability that the poles will be paired correctly (i.e. each hook will hold two poles belonging to the same member)?

I am soooo stuck on these two and I\'m sure I\'m just missing something. Thanks for any help.

Solution

First out of the multiple questions will be answered.

c. There are 11 women for Maria and 3 men for Thomas.

Probability = 11*3 / 16C2 =11/40 = 0.275

d. There are 11 women for Maria, and after Maria pairs with a women, there are 10 women for Thomas.

Probability = 11*10 / 16C2 = 11/12 = 0.9167