Question

Throwing a dice 3 times, where X the combination of total values of 13. What are possible combinations of value 13

Answer 1

Solution

We first note that the same number can appear more than once and up to three times.

The possible combinations are:

1. (1, 6, 6)
2. (2, 5, 6)
3. (3, 4, 6)
4. (3, 5, 5)
5. (4, 4, 5)

Now,

(1) can be arranged in 3 ways, like (1, 6, 6), (6, 1, 6) or (6, 6, 1)

(2) can be arranged in 6 ways, like (2, 5, 6), (2, 6, 5), (5, 2, 6), (5, 6, 2), (6, 2, 5) or (6, 5, 2)

(3) can be arranged in 6 ways, like (3, 4, 6), (3, 6, 4), (4, 6, 3), (4, 3, 6), (6, 4, 3)or (6, 3, 4)

(4) can be arranged in 3 ways, like (3, 5, 5), (5, 5, 3) or (5, 3, 5)

(5) can be arranged in 3 ways, like (4, 4, 5), (4, 5, 4) or (5, 4, 4).

Thus, in total, the possible combinations are: (3 x 3) + (2 x 6)

= 21 Answer

DONE