Exercise · ZW-PERMUTATIONS-AND-COMBINATIONS-008 · ★★★ Advanced
A 5-card hand is dealt from a 52-card deck. What is the probability that it contains all 4 aces?
Choose one option.
Show answer
- D. \(\frac{1}{54145}\)
Explanation
Favorable: the fifth card is any of the other 48. Possible: \(\binom{52}{5}=2{,}598{,}960\). Probability \(\frac{48}{2598960}=\frac{1}{54145}\).
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
- ZW-PERMUTATIONS-AND-COMBINATIONS-001 In how many ways can a president and a secretary be chosen among 5 people (different offices)?
- ZW-PERMUTATIONS-AND-COMBINATIONS-002 In how many ways can a committee of 2 be formed from 6 people?
- ZW-PERMUTATIONS-AND-COMBINATIONS-003 In how many ways can 4 different books be arranged on a shelf?
- ZW-PERMUTATIONS-AND-COMBINATIONS-004 How many different sets of 6 numbers can be chosen from 49, regardless of order?
- ZW-PERMUTATIONS-AND-COMBINATIONS-005 From 5 women and 4 men a committee of 3 is chosen at random. What is the probability it has 2 women…
- 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-009 Which relation between P(n,k) and binomnk is correct?
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