Permutations - Finite Math - Lecture Notes - M118
Permutations
Permutations of k objects selected from n: assuming order matters, the number of ways n! to
select, without replacement, k objects from n is:
p(n,k) = (n-k)!
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Examples:
In a class of 25 students, how many ways can one choose 4 students to win different prizes of $1,
$2, $3, and $4, if……
A) A student cannot be a repeat winner?
P = 25!/254!
P = 303,600
B) Repeat winners are allowed?
254 = 390625
The Greek alphabet consists of 24 letters. How many three letter combinations are possible if….
A) Each letter can be used more than once?
243 = 13824
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Permutations of indistinguishable objects
Consider the word: dog. How many distinguishable ways can the letters be arranged to form a
new 3 letter word?
3P3 = 6
Consider the word: bee. How many distinguishable ways can the letters be arranged to form a
new 3 letter word?
3P3 = 6
FORMULA: The number of distinguishable arranged of nobjects is:
n!/(n1! * n2! *…..nk)
Examples:
