Question

There is a jar of 6 buttons, with one button red, one blue, one purple, one white, one black, and one pink. How many different color combinations can you pull out of the jar if you pull out 2 buttons at the same time?

Answer 1

There is a jar of 6 buttons, with one button red, one blue, one purple, one white, one black, and one pink. How many different color combinations can you pull out of the jar if you pull out 2 buttons at the same time? ​

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Using the expression for the combinations

n = Total observations

r = Number of selected items

`C^n_r=\text{ }\frac{n!}{r!\text{ (n-x)!}}`
`C^6_2=\text{ }(6\cdot5)/(1\cdot2)=\text{ 15}`

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Example

6 options

red (R)

blue (B)

purple (P)

white (W)

black (K)

pink (I)

1. R B

2. R P

3. R W

4. R K

5. R I

6 B P

7 B W

8 B K

9 B I

10 P W

11 P K

12P I

13 W K

14 W I

15 KI

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Answer

Color combinations 15