How many different signals can be made by 5 flags from 8 flags of different colours?

Options

A. `^(8)C_(5)`
B. `^(8)C_(5)xx5!`
C. `5^(8)`
D. `8^(5)`

Answer

B

Explanation

In order to generate singals of 5 flags from 8 flags of different colours, we first select 5 flags from 8 flags. This can be done in `^(8)C_(5)` ways. Now, we arrange selected 5 flags in 5! ways.
Hence, the total number of signals `=^(8)C_(5)xx5!`