1. ## Math question help...........?

Five dice colored (with different colors - blue,green,red,while,black). What is the number of possible outcomes …
a.altogether.
b.in which at least one die shows6?
c.in which exactly one die shows6?
d.what is the number of possible outcomes exactly one die shows 6 and all the dice have same color?

2. Hello, tukilala!

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?
Each die has six outcomes.

Therefore: .$\displaystyle 6^5 \:=\:7776$ possible outcomes.

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

The opposite of "at least one 6" is "no 6s."

There are: .$\displaystyle 5^5 \:=\:3125$ outcomes with no 6s.

Therefore: .$\displaystyle 7776 - 3125 \:=\:4651$ 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: .$\displaystyle 5^4 = 625$ ways.

Therefore: .$\displaystyle 5\cdot5^4 \:=\:3125$ 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?

$\displaystyle P(\text{one 6 and all the same color}) \:=\:0$

3. ## D

I meen in question D, that there is no different between the all 5 dice because they are same color
so........ how can i solve it now???