# Combinations Help

• Jun 18th 2010, 01:28 PM
NeedsHelpp
Combinations Help
In how many ways can 12 prices be awarded evenly among four people?

I am not sure how to start this question.

Also, one more:

From a deck of 52 cards, how many different four-card hands could be dealt which include one from each suit?

Again, I do not know where to start. Additionally, if anyone can link me to a source with more of these combination questions (deck of card questions), that would be great.

Many thanks,

Needs Help
• Jun 18th 2010, 01:42 PM
SpringFan25
Warning My responses to combinations questions are notoriously inaccurate

How many ways can 12 prizes be awarded amongst 4 people.
12!/3!

You know that each person gets 3 prizes.
There are 12! ways of distributing the prizes, and each person gets 3 of them. But the order of the 3 prizes receieved doesn't matter. there are 3! ways of ordering the set of 3 prizes receieved

From a deck of 52, how many 4 card hands include 1 from each suit
There are 4 suits in a standard deck of cards. So you must choose 1 of the 13 spades, then 1 of the 13 clubs,....etc

There are 13*13*13*13 ways of doing that. However the order does not matter so the final answer is

13*13*13*13 / 4!

(there are 4! ways of ordering the 4 suits)
• Jun 18th 2010, 02:17 PM
NeedsHelpp
Quote:

Originally Posted by SpringFan25
Warning My responses to combinations questions are notoriously inaccurate

How many ways can 12 prizes be awarded amongst 4 people.
12!/3!

You know that each person gets 3 prizes.
There are 12! ways of distributing the prizes, and each person gets 3 of them. But the order of the 3 prizes receieved doesn't matter. there are 3! ways of ordering the set of 3 prizes receieved

From a deck of 52, how many 4 card hands include 1 from each suit
There are 4 suits in a standard deck of cards. So you must choose 1 of the 13 spades, then 1 of the 13 clubs,....etc

There are 13*13*13*13 ways of doing that. However the order does not matter so the final answer is

13*13*13*13 / 4!

(there are 4! ways of ordering the 4 suits)

Thanks for the help, however, these are inaccurate. Thanks, though.
• Jun 18th 2010, 02:23 PM
awkward
Quote:

Originally Posted by NeedsHelpp
In how many ways can 12 prices be awarded evenly among four people?

I am not sure how to start this question.

Also, one more:

From a deck of 52 cards, how many different four-card hands could be dealt which include one from each suit?

Again, I do not know where to start. Additionally, if anyone can link me to a source with more of these combination questions (deck of card questions), that would be great.

Many thanks,

Needs Help

12 prizes can be divided evenly among 4 people in

12! / (3!)^4

ways. One way to look at this is as a "multinomial coefficient". Another way is that the prizes can be ordered in 12! ways with person #1 getting 1-3, #2 getting 4-6, etc., but the ordering of gifts for each person doesn't matter.

For the card problem, there are 13 ways to pick a club, 13 ways to pick a spade, etc., so there are 13^4 possible hands. (We don't need to divide by 4! because we specified the suites.)
• Jun 18th 2010, 02:30 PM
SpringFan25
i think ill stop answering these ones :D