in which the product 7 × 6 × 5 × 4 occurs in both terms, and therefore may be removed from both (108), leaving
| 10 × 9 × 8 | , |
| 1 × 2 × 3 |
which is the number of combinations of three out of ten. The same may be shewn in other cases.
EXERCISES.
How many combinations of four can be made out of twelve things?
Answer, 495.
| What number of |  | 6 |  | out of | | 8 | | Answer, | | 28 |
| combinations | 4 | 11 | 330 | |||||||
| can be made of | 26 | 28 | 378 | |||||||
| 6 | 15 | 5005 |
How many combinations can be made of 13 out of 52; or how many different hands may a person hold at the game of whist?
Answer, 635013559600.