How it is calculated
P(n, r) = n! ÷ (n − r)! C(n, r) = n! ÷ (r! (n − r)!) Independent: P(A and B) = P(A)·P(B) P(A or B) = P(A) + P(B) − P(A)·P(B) Binomial: P(X = k) = C(n, k) · p^k · (1 − p)^(n−k)With combinations order does not matter (choosing a team); with permutations it does (ranking winners).
Worked example
Ways to choose 3 people from 10: C(10, 3) = 120. Chance of exactly 3 heads in 5 coin flips: C(5,3) × 0.5⁵ = 31.25%.
Frequently asked questions
Combinations vs permutations?
Permutations count order (AB ≠ BA); combinations do not.
Odds of winning a 6/49 lottery?
1 in C(49,6) = 13,983,816.
What are independent events?
Events where one happening does not change the other’s probability, like two separate dice rolls.