# Solving Combination Problems

There are two questions you have to answer before solving a permutation/combination problem. In other words, can we name an object more than once in our permutation or combination? 3.) How many 3-digit numbers can be formed from the digits 3, 7, 0, 2, and 9?1.) Are we dealing with permutations or combinations? Once we have answered these questions, we use the appropriate formula to solve the problem. Let's look at some examples to get comfortable solving these types of problems. Solution: Let's consider the 3-digit number 702 formed using 3 of the 5 digits.

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Translation: n refers to the number of objects from which the permutation is formed; and r refers to the number of objects used to form the permutation. The permutations were formed from 3 letters (A, B, and C), so n = 3; and each permutation consisted of 2 letters, so r = 2.

For an example that counts permutations, see Sample Problem 1.

If I tell you they crossed the line in the order A, B, C, D, E, this would be different than if I told you they crossed the line in the order C, B, A, E, D.

Thus, the order makes a difference, so the order in which the 5 runners finish is a permutation of the 5 runners. = (20*19*18) / (3*2*1) = 1,140 Therefore, there are 1,140 ways to choose 3 people from a group of 20.

The distinction between a combination and a permutation has to do with the sequence or order in which objects appear.

A permutation, in contrast, focuses on the arrangement of objects with regard to the order in which they are arranged. Using those letters, we can create two 2-letter permutations - AB and BA.

If I said you grabbed those same 5 coins, but I said you grabbed 2 quarters, a nickel, a penny, and a dime, it is still the same group of coins.

That is, the order I name them in is insignificant.

Instructions: To find the answer to a frequently-asked question, simply click on the question.

If none of the questions addresses your need, refer to Stat Trek's tutorial on the rules of counting or visit the Statistics Glossary. A permutation is an arrangement of all or part of a set of objects, with regard to the order of the arrangement.

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