Permutations & Combinations
0/10 problems solved
Formulas & 30-Second Shortcut Tricks
Formulas
- nPr = n!/(n−r)! (order matters)
- nCr = n!/(r!(n−r)!) (order does not matter)
- Arrangements of word with repeats: n!/(p!·q!…)
- Circular arrangements of n: (n−1)!
Shortcuts
- "Arrange / rank / seat" ⇒ permutation; "select / choose / team" ⇒ combination.
- nCr = nC(n−r) — 10C8 = 10C2 = 45.
- Things always together: tie them as one unit, then multiply by internal arrangements.
Practice problems
In how many ways can a committee of 2 be chosen from 7 students?
In how many ways can 5 friends sit around a round table?
How many distinct arrangements of the letters of the word "PEPPER" are possible?
In how many ways can a committee of 3 be chosen from 6 students?
In how many ways can 4 friends sit around a round table?
How many distinct arrangements of the letters of the word "COFFEE" are possible?
In how many ways can a committee of 3 be chosen from 8 students?
In how many ways can 7 friends sit around a round table?
How many distinct arrangements of the letters of the word "SCHOOL" are possible?
In how many ways can a committee of 2 be chosen from 7 students?
Permutations & Combinations Speed Test
1 minute per question. Use the palette to jump around; you'll see time spent on every question at the end.