Suppose we want to choose 4 colors, without replacement, from 17 distinct colors. How many ways can this be done, if the order of the choices is not relevant?

Step-by-step explanation:

The total number of colours is 17.

The number of colours that have to be chosen is 4.

Here, it is given that order is not important. That is, 4 colours can be chosen from the 17 colours in any order.

Since, the order is not important, combinations rule is used to obtain the number of ways in which colours can be chosen among the 17 distinct colours.

The number of different ways in which 4 colours can be chosen among the 17 colours without giving importance to order is obtained as shown below;

17c4=17!/4!=17×16×15×14×13×12×11×10×9×8×7×8×7×6×5=2.48031e13