19.6k views
4 votes
Hello I seem to be having some difficulty with this question can you please help me thank you

Hello I seem to be having some difficulty with this question can you please help me-example-1

1 Answer

1 vote

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:


nCr=(n!)/(r!(n-r)!)

Substitute the values of n and r:


\begin{gathered} nCr=(17!)/(5!(17-5)!) \\ =6188 \end{gathered}

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:


nPr=(n!)/((n-r)!)

Again, substitute the values of r and n:


\begin{gathered} nPr=(n!)/((n-r)!) \\ nPr=(17!)/((17-5)!) \\ =742560 \end{gathered}

When the order is relevant, there could be a total of 752560 ways of choosing 5 colors

User Henry Blyth
by
7.2k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories