A Brief Note on Permutation

Permutation is an arrangement of objects in a definite order.

1). Permutations of different things:

The number of permutations of "n" different things taken "r" at a time

nPr = n(n-1)(n-2)...(n-r+1)

If no repetition occurs:

P(n,r) = n!/(n-r)!

If n = r , P = n!/(n-n)!

P = n!/0! = n!, note: 0! = 1

2). Permutation of n things not all different:

The permutation of "n" at a time in which "q" are alike, "r" are alike and so on:

P = n!/(q!r!)

3. Cyclic Permutation

Cyclic permutations of "n" different things taken "n" at a time is

P = (n -1)!

Sample Problem:

1. How many four-digit numbers can be formed by using the digits 1,2,3,4,6 and 7 if one digit is used only once in a number?

Solution:

P = n!/(n-r)! = 6!/(6-4)! = 6!/2! = 720/2 = 360 ways

2. How many 3 digit numbers can be formed from digits 1,2,3,4,6 and 7 if repetitions are allowed?

Solution:

Since repetitions are allowed each of the three digits can be filled in 6 ways Since there are three digit numbers,

P = 6(6)(6) = 216 ways

Thanks to: Engineering Mathematics Vol.1 by Besavilla

Bonus challenge:

Find the number of permutations which can be formed from the letter PHILIPPINES. Show your process please.