Rolling four six sided fair dice. How to I calculate the probability of rolling only one six and one five?

Question

I’m not sure how to apply the Combination formula to the above question

Answer 1

(6 choose (1,1,4)) (1/6)(1/6)(5/6)^4

 

6!/ (1! * 1! *4!) (1/36)(5/6)^4  <--- definition of multiple combinatoric; (1/6)(1/6) = 1/36

 

= (6*5)/36 (5/6)^4   <---- 4! cancels and combines with 1/36

 

= (30/36) ( 5/6)^4

 

= (5/6)(5/6)^4

 

= (5/6)^5

 

=0.4018775

 

 

It is the same type of problem as finding the number of ways

to arrange the letters in the work STATS

 

There are 2 x S, 2 x T, 1 x A

 

So 5! / (2! 2! 1!) = 5*4*3/ 2 = 30