Exercise · ZW-PERMUTATIONS-AND-COMBINATIONS-001 · ★☆☆ Basic
In how many ways can a president and a secretary be chosen among 5 people (different offices)?
Choose one option.
Show answer
- B. \(20\)
Explanation
Order matters: \(5\cdot4=20=P(5,2)\).
Review the concept: Permutations and combinations
A permutation \(P(n,k)\) is an ordered arrangement of \(k\) elements from a set of \(n\); a combination \(\binom nk\) is a selection in which order does not matter.
\[P(n,k)=\frac{n!}{(n-k)!},\quad \binom{n}{k}=\frac{n!}{k!\,(n-k)!}\]
More practice problems: permutations and combinations
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- ZW-PERMUTATIONS-AND-COMBINATIONS-006 Which of these equals binom103?
- ZW-PERMUTATIONS-AND-COMBINATIONS-007 Five people line up and two of them, A and B, must stand together. In how many ways?
- ZW-PERMUTATIONS-AND-COMBINATIONS-008 A 5-card hand is dealt from a 52-card deck. What is the probability that it contains all 4 aces?
- ZW-PERMUTATIONS-AND-COMBINATIONS-009 Which relation between P(n,k) and binomnk is correct?