5 of the 7 letters \(\mathrm { A } , \mathrm { B } , \mathrm { C } , \mathrm { D } , \mathrm { E } , \mathrm { F } , \mathrm { G }\) are arranged in a random order in a straight line.
(a) How many different arrangements of 5 letters are possible?
(b) How many of these arrangements end with a vowel (A or E)?
A group of 5 people is to be chosen from a list of 7 people.
(a) How many different groups of 5 people can be chosen?
(b) The list of 7 people includes Jill and Jo. A group of 5 people is chosen at random from the list. Given that either Jill and Jo are both chosen or neither of them is chosen, find the probability that both of them are chosen.