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
[tex]\binom{n}{r}=\frac{n!}{r!(n-r)!}[/tex]
[tex]\binom{7}{4}=\frac{7!}{4!(7-4)!}[/tex]
[tex]\binom{7}{4}=\frac{7\times 6\times 5\times 4!}{4!\cdot3\times2}[/tex]
Hence, total possible different numbers of token of given type =35
