There is one question I don't understand.
A bin contains 5 matched pairs of gloves. Each matched pair contains a left hand and a right hand glove that match. In how many ways can 4 gloves be taken from the bin without including a matched pair?
Possible answers: 160, 120, 80, 40, 30
But since you want the number of combinations without matching pairs, you need to realise that there are 5 matching pairs, so the number of non-matching pairs are
The question says that we choose 4 gloves from 10 though.
Here's my best answer
Total ways of choosing 4 from 10:
Number of ways of choosing TWO pairs of gloves (we don't want this):
Number of ways of choosing ONE pair of gloves (we don't want this either):
* * 2^2 = 130
Total ways = 210 - 10 - 130 = 80