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calling carol vorderman, or other eggheads! help needing with a numbers competition



desprateseagull

New member
Jul 20, 2003
10,171
brighton, actually
http://forums.moneysavingexpert.com/showthread.php?t=4910592 to win £200 amazon vouchers..


Solve the brainbuster and win £200 of Amazon vouchers to spend on high-tech.

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.

The competition closes on Sunday 30th March 2014.

http://www.ecmselection.co.uk/brainb...-team-building
 


teaboy

Well-known member
Jul 5, 2003
1,840
My house
http://forums.moneysavingexpert.com/showthread.php?t=4910592 to win £200 amazon vouchers..


Solve the brainbuster and win £200 of Amazon vouchers to spend on high-tech.

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.

The competition closes on Sunday 30th March 2014.

http://www.ecmselection.co.uk/brainb...-team-building

Is there anything stipulating that the highly experienced developers are not also graduates?
 


happypig

Staring at the rude boys
May 23, 2009
7,934
Eastbourne
you have to pick 5 graduates from a pool of 9 and 6 developers from a pool of 8

For graduates, there are 9 you can pick first, then 8 left so the graduates will be 9*8*7*6*5 = 15120
for developers its 8*7*6*5*4*3 = 20160

multiplied together = 304819200
 




Goldstone1976

We Got Calde in!!
Helpful Moderator
NSC Patreon
Apr 30, 2013
13,763
Herts
It's two separate combinations, not a permutation from two sets.

So, for each combination you use C (n,k) = n!/(n-k)!k!.

Set 1= Developers

C = 8!/(8-6)!6!

= 8!/2!6!

= 40320/2x720

=40320/1440

= 28

Set 2 = Graduates

C=9!/(9-5)!5!

=9!/4!5!

= 362880/24x120

=362880/2880

= 126

Finally, Since any one of the 28 combinations of developers can have any one of the 126 combinations of graduates, you multiply the two together

126x28 = 3528.

It's important to distinguish combinations (where the order doesnt matter) to permutations (where the order does matter). Here, since it doesn't matter whether developer (or graduate) A, B, C etc is chosen, just that the required total is, it's a combination, not a permutation.
 






The Andy Naylor Fan Club

Well-known member
Aug 31, 2012
5,144
Right Here, Right Now
3,528

There are 126 possible combinations of teams of Five graduates

There are 28 possible combinations of teams of Six experienced developers

Multiply 126 x 28 = 3,528

The way of solving the combinations is by taking your total numbers of grads ( 9 ) and using countback multiply by how many are to be in each team ( 5 ).

So, 9 x 8 x 7 x 6 x 5 = 15,120

Then you divide by multiplying counting forward from ( 1 ) the number that are in each team, again ( 5 ).

1 x 2 x 3 x 4 x 5 = 120

15,120 ÷ 120 = 126

Using the same format ( 8 ) developers in groups of ( 6 )

8 x 7 x 6 x 5 x 4 x 3 = 20,160

1x 2 x 3 x 4 x 5 x 6 = 720

20, 160 ÷ 720 = 28

Bugger, just seen the same answer above. That'll teach me for not pressing the submit button and then checking my emails.
 



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