Permutations Homework

In mathematics, the notion of permutation is used with several slightly different meanings; all related to the act of permuting that is rearranging, several objects or values. Informally, a permutation of a set of values is an arrangement of those values into a particular order. Thus there are six permutations of the set {1,2,3}, namely [1,2,3], [1,3,2], [2,1,3], [2,3,1], [3,1,2], and [3,2,1].

In this article, permutation examples and homework problems are given.

Formula and examples for permutations homework:

If 'k' is the number of possible permutations from a set of 'n' then this is usually written nPk .
n!
Formula: nPk = ---------------- = n(n-1)(n-2)…(n-k+1)
(n-k)!


Example problems for algebra:

Ex:1) How many three-digit values can be positioned from the digits 3, 4, 5, 6, and 7, if each digit is unique?

Sol:

Counting the values of permutations(P) of 5 unique objects, taken 3 at a time. The number of permutations (P) of n unique objects, taken r at a time is

nPr = n! / (n - r)!

5P3 = 5! / (5 - 3)! = 5! / 2! = 5x4x3 = 60

Thus, 60 different 3-digit numbers can be formed from the digits 3, 4, 5, 6, and 9.

Ex:2) How many 3-letters can be arranged from the letters a-z, if each letters is distinct?

Sol:

Counting the number of permutations(P) of 26 distinct letters, taken 3 at a time. The number of permutations (P) of n distinct objects, taken r at a time is

nPr = n! / (n-r)!

n = 26, r = 3

26P3 = 26! / (26-3)! = 26! / 23! = 26x25x24 = 15600.

Thus, 15600 different 3-letters can be formed from the letters a-z.

Ex:3) Find the number of the ways to select and rank favorite 5 days of the year.

Sol:

n = 365, r = 5

nPr = n! / (n-r)!

365P5 = 365! / (365!-5!) = 365! / 360! = 365 x 364 x 363 x 362 x 361= 6302555018760

Thus, 6302555018760 different 5-days can be formed from the year.

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Homework problems for permutations:

Homework problem 1: How many ways can a chairman, a treasurer and a secretary be chosen from among 7 candidates?

Ans: 210 ways

Homework problem 2: A word begins with three letters. If the possible letters are P, Q, R, S and T, how many different permutations of these letters can be made if no letter is used more than once?

Ans: 60