Counting: Permutations & Combinations (Discrete Mathematics)
Free printable Discrete Mathematics worksheet on counting principles: when order matters (permutations) versus when it does not (combinations), committee and race problems, and the identity C(n, r) = P(n, r)/r!. Every value computed by exact nPr and nCr arithmetic.
✓ Answer key checked by math, never wrong
Discrete Mathematics · Math worksheet
Name
Date
Math
Counting: Permutations & Combinations
First decide whether order matters. Ordered selections (codes, rankings, arrangements) are permutations: P(n, r) = n!/(n - r)!. Unordered selections (committees, handshakes, lottery draws) are combinations: C(n, r) = n!/(r!(n - r)!). The two are linked by C(n, r) = P(n, r)/r!.
- 1.Evaluate P(8, 3), the number of permutations of 3 objects chosen from 8 distinct objects.
- 2.Evaluate P(9, 3), the number of permutations of 3 objects chosen from 9 distinct objects.
- 3.Evaluate C(7, 3), the number of combinations of 3 objects chosen from 7 distinct objects.
- 4.Evaluate C(8, 3), the number of combinations of 3 objects chosen from 8 distinct objects.
- 5.A club has 11 members. How many different 3-person committees can be formed? (Committee members have equal roles.)
- 6.8 runners enter a race. In how many different ways can the gold, silver, and bronze medals be awarded?
- 7.In how many ways can 4 of 6 different books be arranged in a row on a shelf?
- 8.At a meeting of 12 people, every pair of people shakes hands exactly once. How many handshakes take place?
- 9.Permutation or combination: which counts the number of ways of choosing a 4-digit door code whose digits are all different?
- a) Permutation
- b) Combination
- 10.Permutation or combination: which counts the number of ways of picking 6 lottery numbers from 49?
- a) Permutation
- b) Combination
- 11.Every combination of 3 objects can be ordered in 3! = 6 ways, so C(8, 3) = P(8, 3)/3!. Evaluate C(8, 3) this way.
Made with ChalkBee · chalkbee.com