How many possible menus can be created with 10 foods from 4 categories?

  • Thread starter majorlag
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In summary, a combinatoric problem is a mathematical problem that involves counting and organizing objects or events. Common strategies for solving these problems include using permutations and combinations, creating systematic lists or tables, and using visual aids like Venn diagrams. The main difference between a permutation and a combination is that a permutation considers the order of selection, while a combination does not. Combinatoric principles can be applied in various real-life situations, such as probability problems and computer programming. Some common mistakes to avoid when solving combinatoric problems include forgetting to consider all possible outcomes, double-counting, and confusing permutations and combinations. It is important to carefully define the problem and understand its context before attempting to solve it.
  • #1
majorlag
2
0
I need help on how to solve these homework problems.

1. Coefficient of x^12 in (1+x^2)(1-x)^-10


2.Find a generating function for the problem: there are 4 food categories, each category comprising of 20 distinct foods. Ten foods with at least one from each category is to be selected. how many menus are possible?
 
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  • #2
1. Just do it; you know the expansion of (1-x)^{-10} and that is all that you need.
 
  • #3
is the answer C(22,10)?
 

FAQ: How many possible menus can be created with 10 foods from 4 categories?

What is a combinatoric problem?

A combinatoric problem is a type of mathematical problem that involves counting and organizing objects or events. These problems typically involve finding the number of ways in which a certain outcome can occur.

What are some common strategies for solving combinatoric problems?

Some common strategies for solving combinatoric problems include using permutations and combinations, creating a systematic list or table, and using the Binomial Theorem. Other strategies may involve using visual aids such as Venn diagrams or tree diagrams.

What is the difference between a permutation and a combination?

A permutation is an ordered arrangement of a set of objects or events, while a combination is an unordered selection of a subset of those objects or events. In other words, a permutation considers the order in which the elements are selected, while a combination does not.

How can I apply combinatoric principles in real-life situations?

Combinatoric principles can be applied in a variety of real-life situations, such as in probability problems, creating schedules or seating arrangements, and in computer programming. For example, combinatorics is often used in coding to generate all possible combinations of characters for a password.

What are some common mistakes to avoid when solving combinatoric problems?

Some common mistakes to avoid when solving combinatoric problems include forgetting to consider all possible outcomes, double-counting, and confusing permutations and combinations. It is also important to carefully define the problem and understand the context in which it is being presented.

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