Question

question 22
suppose a designer has a palette of 8 colors to work with, and wants to design a flag with 2 vertical stripes, all of different colors.
how many possible flags can be created?
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Explanation:

Step1: Identify the problem type

This is a permutation problem since the order of colors (stripes) matters (different order of colors gives a different flag). The formula for permutations of \( n \) items taken \( r \) at a time is \( P(n, r)=\frac{n!}{(n - r)!} \), or equivalently \( P(n, r)=n\times(n - 1)\times\cdots\times(n - r+1) \). Here, \( n = 8 \) (total colors) and \( r = 2 \) (number of stripes).

Step2: Calculate the number of permutations

For \( n = 8 \) and \( r = 2 \), we use the formula \( P(8, 2)=8\times(8 - 1) \).
First, calculate \( 8-1 = 7 \).
Then, multiply \( 8\times7 = 56 \).

Answer:

56