Solving Combination Problems

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

Note that AB and BA are considered to be one combination, because the order in which objects are selected does not matter.

A permutation, in contrast, focuses on the arrangement of objects with regard to the order in which they are arranged.

For an example that counts the number of combinations, see Sample Problem 2.

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.Each possible selection would be an example of a combination.The complete list of possible selections would be: AB, AC, and BC.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.This is the key distinction between a combination and a permutation.A combination focuses on the selection of objects without regard to the order in which they are selected.Each possible arrangement would be an example of a permutation.The complete list of possible permutations would be: AB, AC, BA, BC, CA, and CB.Both permutations and combinations are groups or arrangements of objects. When dealing with combinations, the order of the objects is insignificant, whereas in permutations the order of the objects makes a difference.For example, assume you have 10 coins in your pocket and you take 5 out, a dime, 2 quarters, a nickel and a penny.