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

the ratio of white tiles to blue tiles is 48: 16. the ratio in it's simplest form is 3: 1.

step-by-step explanation:

ratio: take the first number and add a colon next to it, then add the second number after that. make sure the ratio order matches up with the written problem!

simplest form: we can simplify the ratio 48 : 16 by dividing both terms by the greatest common factor (gcf).

the gcf of 48 and 16 is 16.

divide both terms by 16:

48 ÷ 16 = 3

16 ÷ 16 = 1

reducing to simplest form:

48 : 16 = 3 : 1