CHEN 3010
Applied Data Analysis
Names
Fall 2022
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Workshop 2: Permutations and Combinations
Each group should have 8 lettered cubes.
1. Select 3 of your cubes. By hand, determine how many permutations can be made with these 3
cubes. Make and write down each arrangement in the space below.
How many permutations can be made with 4 cubes? Write down each arrangement in the space
below. What is the relationship between the number of permutations of r distinct objects and r+1
distinct objects?
2. How many permutations can be made using all the cubes in your set?
3. If three of your pieces were identical, how many arrangements would be possible?
CHEN 3010
Workshop 3
Page 2
4. Select 5 of your 8 cubes at random. Using the 5 cubes, select all the possible combinations of 3
cubes. Write each combination down. Remember, the order of the 3 cubes selected is not
important (ABC is the same as CBA). How many combinations are there?
For each of your combinations, how many permutations are there? Consequently, how many total
permutations are there?
Calculate the number of permutations and combinations using the formulas to confirm your
answers above.