Question

How many ways? can 4 person is throwing a dice. Make a sum of 6

Answer 1

See below.

Explanation:

`s_1={1,1,1,3}` and `s_2={1,1,2,2}` are the possible sets which add up to `6`

now with `s_1` we can form `{1,1,1,3},{1,1,3,1},{1,3,1,1},{3,1,1,1}` then `abs (s_1) = 4`

Is left as an exercise the calculus of `abs(s_2)` and then the answer is

`n = abs(s_1)+abs(s_2)`

Answer 2

There are 10 ways.

Explanation:

There are two possible sets of rolls: `{1,1,1,3}` and `{1,1,2,2}.`

Set 1:
Of the four people, three roll a 1 and one rolls a 3. The total ways to arrange these rolls among 4 people is

`(4!)/(3!*1!)=24/(6xx1)=4`

Set 2:
Of the four people, two roll a 1 and two roll a 2. The total ways to arrange these rolls among 4 people is

`(4!)/(2!*2!)=24/(2xx2)=6`

Total:
The total number of ways that 4 people can each roll a die with the sum being 6 is:

`4+6=10`