Hello, tukilala!

Each die has six outcomes.Five dice with different colors: blue, green, red, while, black.

I must assume that all five dice are rolled at once.

What is the number of possible outcomes …

(a) altogether?

Therefore: . possible outcomes.

(b) in which at least one die shows 6?

The opposite of "at least one 6" is "no6s."

There are: . outcomes with no 6s.

Therefore: . outcomes with at least one 6.

(c) in which exactly one die shows 6?

There are 5 choices of a die to show the 6.

The other 4 dice must show one of the other numbers: . ways.

Therefore: . ways to get exactly one 6.

(d) What is the number of possible outcomes exactly one die shows 6

and all the dice have same color? . . . . what?