A coach is to select a basketball team from a group of 9 people.

Question

A coach is to select a basketball team from a group of 9 people. If the team consists of 2 forwards, 2 guards, and 1 center, how many such teams are possible?

A. 52
B. 3780
C. 7560
D. 15120
E. 11664

woohoo921 · Answer

MartyTargetTestPrep

I realize that this can best be solved with an anagram, but I tried to use the combination formula:

9!/(2!)(7!) * 9!/(2!)(7!) * 9!/8!

However, this is not the right answer. How would you solve this using the combination (or permutation formula if I am incorrect in using the combination formula)?

Thank you for all of your time and help.

MartyTargetTestPrep · Answer

You need to take into account that you don't have 9 people to choose from after you have chosen the forwards, and that you don't have 7 people to choose from after you have chosen the guards.

So, what you have is mostly correct, but you need to adjust it to take into account that you are working with fewer people in each step after the first. See what happens when you make that adjustment.

Rainman91 · Answer

answer is 52?

9C1 + 8C2 + 6C2 = 52.

jim441 · Answer

Total People = 9
Required = 5

Ans = selection*arrangement ( arragement coz any player can be designated any position)

9C5*5!
9!/4!

In my opinion ans = 15120. Kindly validate

Regor60 · Answer

This approach counts as arrangements the two forwards and two guards switching "positions" within their roles as same.

Posted from my mobile device

jim441 · Answer

Oh yeah you are right,the correct answer would be:

9C5*5!/(2!*2!)

woohoo921 · Answer

Got the answer to match!
(9!/2!7!)*(7!/2!5!)*(5!/4!)=3,780

You rock!!!

MartyTargetTestPrep · Answer

Well done!

Anki111 · Answer

Easy one. 9c2x7c2x5c1 =3780. After selecting the forwards, you have to select from remaining and same way the next time.

Natansha · Answer

Hi  KarishmaB  in this we are getting the right ans by doing 9C2 * 7C2 * 5C1 = 3780 but don't we need to divide it by 2! as we do when:

distributing 4 people in groups of 2 each = 4C2/2!

to correct for the repeat groups here?

KarishmaB · Answer

In that case, the groups are identical. They are not "named" so to say. So from A, B, C, D, when I select 2 people, I can do it by selecting A, B giving me 2 groups as A, B and C, D or I can select C, D giving me two groups are A, B and C, D. This is double counting and hence division by 2.

But here, we select 9C2 for Forward positions so we select A, B for Forwards and 7C2 for guards so C, D for guards.
If I select C, D for Forward and A,B for guards, these are different selections. Hence there is no double counting here. Hence no division by 2!

A coach is to select a basketball team from a group of 9 people.

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A coach is to select a basketball team from a group of 9 people.

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