Combinations

What Combinations is

Combinations are a way of selecting items from a larger set in which the order of the items is not important.

Steps for Combinations:

  1. Determine the number of items you are selecting from (n).

  2. Choose the number of items to be selected (r).

  3. Calculate the number of possible combinations using the formula C(n,r) = n! / (r!(n-r)!).

  4. List out all of the possible combinations.

  5. If desired, cross off unwanted combinations.

  6. Count the number of remaining combinations to get the final answer.

Examples

  1. Combinations can be used in analyzing gene sequences in order to identify patterns that are likely to be associated with certain traits or diseases.

  2. Combinations can be used in analyzing survey data to identify the most common combinations of responses to particular questions.

  3. Combinations can be used in calculating sample sizes for experiments when the number of combinations of factors is too large to be considered exhaustively.

  4. Combinations can be used to identify the most profitable combinations of investments for a portfolio.

  5. Combinations can be used to identify the most efficient routes for traveling from one location to another.

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