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

Answer:

35

Step-by-step 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

$\binom{n}{r}=\frac{n!}{r!(n-r)!}$

$\binom{7}{4}=\frac{7!}{4!(7-4)!}$

$\binom{7}{4}=\frac{7\times 6\times 5\times 4!}{4!\cdot3\times2}$

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