Answer:
a. 6188 ways
b. 752560 ways
We need to find how many ways we can choose 5 colors from 17 distinct colors.
From this we know that:
n = total number of colors in the set = 17
r = number of choosing colors = 5
If the choices are not relevant, we will use Combination which is noted as:
[tex]nCr=\frac{n!}{r!(n-r)!}[/tex]
Substitute the values of n and r:
[tex]\begin{gathered} nCr=\frac{17!}{5!(17-5)!} \\ =6188 \end{gathered}[/tex]
When the order of choices is not relevant, there are 6188 ways to choose 5 colors out of 17.
Now, if the order of choices is relevant, we will use permutation which is noted as:
[tex]nPr=\frac{n!}{(n-r)!}[/tex]
Again, substitute the values of r and n:
[tex]\begin{gathered} nPr=\frac{n!}{(n-r)!} \\ nPr=\frac{17!}{(17-5)!} \\ =742560 \end{gathered}[/tex]
When the order is relevant, there could be a total of 752560 ways of choosing 5 colors
