## The brainbuster

A high-tech company has 17 engineers: nine graduates and eight experienced developers.

For a large new project, they want to put together a project team comprising six experienced developers and five graduates.

How many different possible teams are there?

Show your workings. Only complete entry forms will be considered. The judge's decision is final.

This competition closed on Sunday 30th March 2014.

## The entries

We had quite a lot of responses, which mostly gave the correct answer, which equates to 126 * 28. One entrant though decided to add the numbers for the two teams together, rather than multiply them...

And as usual not everyone followed the instructions completely.

## The solution

Here is the answer as given by our winner:

There are 3528 different possible teams. I used the combination formula for selecting objects (or people!) from a set where the order is irrelevant:

`C(n,x) = n!/(n-x)!*x!`

, where`n`

is the size of the set and`x`

is the number of objects selected.Number of combinations of choosing 6 experienced developers from 8:

`8C6 (n=8,x=6) = 8*7*6*5*4*3/6*5*4*3*2 = 8*7/2 = 28`

Number of combinations of choosing 5 graduates from 9:

`9C5 = 9*8*7*6*5/5*4*3*2 = 3*7*6 = 126`

Therefore the total number of possible combinations is

`8C6 * 9C5 = 126*28 = 3528`

.

## And the winner is...

The winner of ecm's brainbuster no. 36 is Rebecca White, who is studying for her PhD in Physics at the University of Warwick. Rebecca wins £200 of Amazon vouchers to spend on high-tech.

Congratulations again to Rebecca, and watch out for ecm's next brainbuster !