Practice Permutation in Math
Use these practice problems to test your method after reviewing the concept explanation and worked examples.
Quick Recap
A permutation is an ordered arrangement of objects — the number of ways to choose and order items from distinct items is .
With permutations, order matters — first place and second place are different. Think of ranking students: ABC and BAC are different orderings.
Showing a random 20 of 50 problems.
Example 1
hardIn how many ways can different books be arranged on a shelf if specific books must always stand together?
Example 2
mediumCompute .
Example 3
easyHow many ways can 3 distinct books be arranged on a shelf?
Example 4
hardA license plate has letters (no repeats, from ) followed by digits (no repeats, from –). How many such plates exist?
Example 5
challengeHow many ways can different beads be arranged on a circular bracelet, treating rotations AND reflections as the same?
Example 6
easyDoes in general?
Example 7
challengeIn how many ways can the letters of be arranged so that the two 's are NOT adjacent?
Example 8
easyCompute .
Example 9
easyCompute .
Example 10
mediumHow many 3-digit numbers (no repeated digits) can be formed from ?
Example 11
mediumSolve for : .
Example 12
mediumHow many -letter words (real or nonsense) can be formed from with no repeats?
Example 13
mediumA club of students must choose a president, vice president, and secretary. In how many ways can the officers be chosen?
Example 14
easyCompute .
Example 15
hardHow many ways can people sit in a row if two specific people refuse to sit next to each other?
Example 16
easyTrue or false: .
Example 17
easyHow many 2-letter ordered codes (no repeats) use letters from ?
Example 18
mediumHow many ways can the letters of be arranged?
Example 19
easyIn how many ways can medals (gold, silver, bronze) be awarded to runners?
Example 20
easyCompute .