# Thread: Number of Trios Help

1. ## Number of Trios Help

Hi i would like some help on this particular question finding it hard to do can any generous person pls pls help would appreciate there kindness
Thank you

1. Three whole numbrs, greater than zero, can be used to form a trio.
for example (1,2,2) is a trio whose sum is 1+2+2=5
and
(2,1,2) is a different trio whose sum is also 5.

How many trios can you find with a sum of 5?

Investigate further

2. What you want to count is: the number of ways to place 5 identical items into three different positions such that no position is empty.
That is a combination: C([5-3]+[3-1],[5-3])=C(4,2)=6.
See if you can list all six of these to convince yourself. Are there more?

I wrote the way I did to help you generalize on 5=n.

3. Hello, nbukhar!

1. Three positive integers can be used to form a trio.
For example (1,2,2) is a trio whose sum is 1 + 2 + 2 = 5
and (2,1,2) is a different trio whose sum is also 5.

How many trios can you find with a sum of 5?
The very least you can do is list the trios. .Did you try?

There are six: .(1,2,2), (2,1,2), (2,2,1), (1,1,3), (1,3,1), (3,1,1)

I assume "Investigate further" means to try to generalize the problem.

For example, how trios have a sum of 7?

Consider a 7-foot board, marked at intervals of one foot.
We want to cut it into three pieces.
Code:
    * - * - * - * - * - * - * - *
|   |   |   |   |   |   |   |
* - * - * - * - * - * - * - *
↑   ↑   ↑   ↑   ↑   ↑
There are 6 places to make the cuts; we will choose 2 of them.
. . Hence, there are: C(6,2) = 15 choices.

Therefore, there are 15 trios with a sum of 7.

In general, for a whole number n > 3, there are: .C(n-1, 2) trios.