| 3.a) The number of ways to choose 3 questions out of a total of 10 is | ( |
10 | ) | = |
10! | = |
120. |
| 3 | 3! 7! |
Hence there are 120 possible combinations of 3 words that you could pick.
b) Think of having three positions and consider the number of possibilities for each choice.
| first word | second word | third word |
| 10 | 9 | 8 |
When the order of the words matters, there are 10 · 9 · 8 = 720 possible sets of 3 words that you could pick.
c) The answer to part a) was C(10,3) and the answer to part b) was P(10,3). The answer to part b) is 3! times the answer to part a) since there are 3! ways to arrange the three words amongst themselves. In general P(n,r) = r! C(n,r).