AS Stats probability problem?

Question

1) The probability of obtaining a double when 2 fair dice are thrown is 1/6. Four players play a board game which requires them to take it in turns to throw two fair dice. Each player throws the 2 dice once in each round. When a double is thrown the player moves forward six squares. Otherwise player moves on square. Find

a) Probability that exactly one of the four players obtains a double in the first round.

b) The probability that a double occurs exactly once in 4 of first 5 rounds.

Answer 1

a. Binomial Distribution

  4C1 = 4

  (4)(1/6)^1 X (5/6)^3

= 0.385802

b.  5C4 = 5

    (5) (.3858)^4 X (1 - .3858)^1  

= 0.026248  

If you haven't learned this yet you will and its a ***** the other way.  You have to figure out Combinations of success divided by total combinations and I don't know how to do that with this problem.

Answer 2

a)4C1(1/6)[(5/6)^3]

b)5C4{4C1(1/6)[(5/6)^3]}