Then take the natural series 1, 2, 3, &c., up to the number of things to be taken at a time, and find the product of all the terms of this series.
Divide the former product by the latter, and the quotient will be the answer.
How many combinations of 3 numbers can be taken out of 78 numbers?
| 78×77×76 = | 456456 and |
| 1×2×3 = | 6 |
| 6)456456 | |
| 76076 | Answer. |
How many combinations of 3 numbers can be taken out of 70 numbers?
| 70×69×68 = | 328440 and |
| 1×2×3 = | 6 |
| 6)328440 | |
| 54740 | Answer. |
How many combinations of 3 numbers can be taken out of 60 numbers?
| 60×59×58 = | 205320 and |
| 1×2×3 = | 6 |
| 6)205320 | |
| 34220 | Answer. |
How many combinations of 3 numbers can be taken out of 40 numbers?
| 40×39×38 = | 59280 and |
| 1×2×3 = | 6 |
| 6)59280 | |
| 9880 | Answer. |