How Many Ways to Split Students and Combine Outfits?

In summary, the conversation discusses two problems involving combinations and permutations. For the first problem, there are 12 students divided into three rooms, and the number of ways this can happen is calculated using combinations. For the second problem, the number of different outfits that can be made from 6 pairs of jeans, 3 shirts, and 2 pairs of sandals is calculated using combinations and permutations. The final answer is 36.
  • #1
Apophis
4
0
:rolleyes: I can normally do combinations and permutations, but these two currently stump me. Any help is appreciated. :confused:

1) Twelve students are in a class. They are split so that five go to room A, four go to room B and three go to room C. How many different ways can this happen?

2) You have six pairs of jeans, three shirts and two pairs of sandals. How many different outfits can you wear from these choices?

:rolleyes:
 
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  • #2
For number two, I think (2c1)(3c1)(6c1) describes the correct answer. There are 36 combinations. Thats evaluated as

[tex] nCk = \frac{n!}{k!(n-k)!} [/tex]
 
  • #3
For The First One:

[itex] (12C_5)(7C_4)(3C_3) [/itex]

For The Second One:

Take One Shirt ===> You can pair it up with 6 different jeans
And each of the above pair of shirt+jeans can be worn in two way (with 2 different pairs of sandals) Therefore total cases=

(1 x 6) x 2 =12

Similarily the above case happenes 3 times for three different shirts :

12 x 3

Ans= 36
 
  • #4
Thank You

Thank You all for the help. This makes more sense to me now. :biggrin:
 

Related to How Many Ways to Split Students and Combine Outfits?

What is the difference between combinations and permutations?

Combinations are ways of selecting objects from a group without considering the order, while permutations are ways of arranging objects in a specific order.

How do I calculate the number of combinations or permutations?

The number of combinations is calculated by using the formula nCr = n! / (r!(n-r)!), where n is the total number of objects and r is the number of objects being selected. The number of permutations is calculated by using the formula nPr = n! / (n-r)!, where n is the total number of objects and r is the number of objects being arranged.

What is the significance of combinations and permutations in real life?

Combinations and permutations are used in various fields such as mathematics, statistics, and computer science to solve problems involving probability, counting, and data analysis. They are also applied in real-life situations such as lottery games, sports tournaments, and genetics.

What are some common mistakes people make when dealing with combinations and permutations?

Some common mistakes people make include confusing combinations with permutations, not using the correct formula, and not considering all possible outcomes. It is also important to carefully define the problem and understand the context in which combinations and permutations are being used.

How can I improve my skills in solving problems involving combinations and permutations?

Practice is key to improving your skills in solving problems involving combinations and permutations. It is also important to understand the underlying concepts and formulas, and to carefully read and interpret the problem before attempting to solve it.

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