pdf Combinations B

This worksheet provides focused practice with combinations through engaging real-world story problems. Students apply the combinations formula \(nCr=\frac{n!}{r!(n-r)!}\) to determine how many different groups can be formed when order does not matter. Each problem reinforces the idea that selecting items in a different order does not create a new combination.

Scenarios include selecting basketball starters, choosing students for conferences, combining letters from a word, selecting ingredients, choosing colored pencils, picking cookie flavors, and mixing sodas. Students must identify the total number of items \(n\) and the number being chosen \(r\), substitute correctly into the formula, and simplify factorial expressions efficiently.

Because every problem is presented in context, students strengthen both procedural fluency and conceptual understanding of counting principles. The consistent emphasis on order not being important reinforces the distinction between combinations and permutations.

Skills Assessed

• Applying the combinations formula \(nCr=\frac{n!}{r!(n-r)!}\)

• Identifying appropriate values for \(n\) and \(r\)

• Simplifying factorial expressions

• Interpreting real-world counting scenarios

• Distinguishing combinations from permutations

• Strengthening combinatorial reasoning

Classroom Use

This worksheet works well as guided practice when introducing combinations, independent practice in a probability unit, or review before an assessment on counting principles. It is also effective for reinforcing factorial simplification skills in algebra or precalculus courses.

Details

• 2 pages

• Answer key included

ID# 0235