Question

Suppose we want to choose 6 colors if the order is taken from  9 distinct colors

how many ways could this be done if the order of the choices is taken into consideration?

how many ways can this be done if the order choices is not taken into consideration?

Answer 1

We want to choose 6 colours from 9 distinct colours.

When the order is taken into consideration, we take a permutation of the 6 colours among 9 colours.

Number of ways this can be done = 9P6

= (9 !)/(9-6)!

= 9 * 8 * 7 * 6 * 5 * 4 = 60480

When the order is taken into consideration, this can be done in 60480 ways.

When the order is not taken into consideration, we take a combination of the 6 colours among 9 colours.

Number of ways this can be done = 9C6

= (9 !)/{(9-6)! * 6!}

= 9! / (6! * 3!) = 84

When the order is not taken into consideration, this can be done in 84 ways.