Question

Jean has 5 different colors of markers: red, blue, green, orange, and purple. Two colors are used to make a sign. How many different combinations are possible? List them.

Answer 1

We need to find the number of possible combinations of r objects from a set of n objects. 
Jean has 5 different colors which means that n=5 and 2 colors are used to make a sign, which means r=2.
The number of combinations can be calculated with the formula: 
C=n!/((n-r)!r!)
C=5!/(5-2)!*2!
C=5*4*3!/3!*2*1
C=20/2=10
The possible combinations are:
1.red blue
2.red green
3.red orange
4.red purple
5. blue green
6. blue orange
7. blue purple
8. green orange
9. green purple
10. orange purple