Question

A certain board game uses tokens made of transparent colored plastic. Each token looks like where each of the four different regions is a different color: either red, green, yellow, blue, orange, purple, or black. How many different tokens of this type are possible? (Note: The white circle is a region.)

Answer 1

35

Explanation:

We are given that a certain board game uses token made of transparent colored plastic.

Each token looks like where each of the four different regions is a different color.

We have to find out number of tokens of this type are possible

Given colors are red,green,yellow,blue,orange,purple and black.

Total number of colors=7

We have to select four colors out of seven colors

n=7,r=4

Using combination formula

`\binom{n}{r}=(n!)/(r!(n-r)!)`

`\binom{7}{4}=(7!)/(4!(7-4)!)`

`\binom{7}{4}=(7* 6* 5* 4!)/(4!\cdot3*2)`

Hence, total possible different numbers of token of given type =35