What Are the Probabilities of Different Dice Combinations in a Single Roll?

[Susan0814]

When rolling 5 dice one time for each, what is the formula to figure the probability of getting a 5 of a kind, 4 of a kind, 3 of a kind, pair, and a straight.
I used 6*(1/6*1/6*1/6*1/6*1/6) to get the probability of 5 of a kind and came up with 6/7776. What formulas do I use to get the others or how do I alter the formula?

 

[Dick]

You are off to a good start. The formula is (how many kinds)*(probability of getting n of the kind)*(how many ways to get the n). You've correctly done the five of a kind as 6*(1/6)^5*1. Now let's do 4. The first number is the same. The second number becomes (1/6)^4*(5/6) (four must be the selected number and the fifth can't). The last number is how many ways can this happen. Any of the 5 numbers can be nonmatching so 5. So 6*(1/6)^5*(5/6)*5. You can creatively make these up for each case, or you can think of some general formula you've been taught to apply. Hint: one of the numbers is called a combinatorial coefficient.