Permutation problems can be quite challenging, but with the right guidance and practice, they become manageable. In this article, we’ll tackle several examples of permutation problems, and provide additional practice questions for you to work on.
What Exactly is a Permutation?
The term permutation is used to describe the process of arranging a set of objects in a specific order. The formula for permutation is:
n
P
r
= n!/(n – r)!
For a more in-depth understanding of permutation, check out this
article
.
Examples of Permutation Problems and Solutions
1. Determine the following:
(i)
n
P
r
when n = 10, r = 4
(ii)
8
P
3
2. How many different ways can the letters of the word LEARNING be arranged so that the vowels always come together?
3. In how many ways can five books be arranged on a shelf?
4. How many different arrangements of letters of the word STATISTICS are possible?
5. How many 4-digit even numbers can be made using the digits 1, 2, 3, 4, 6, and 7 if no digit is repeated?
Practice Problems on Permutation
How many ways can the letters of the word “MOTIVATION” be arranged such that the first and last letters are the same, and the vowels are together?
How many numbers between 200 and 2000 use only even digits, no digit being repeated?
How many 3-letter words, with or without meaning, can be formed out of the letters of the word ALGORITHMS, if repetition of letters is not allowed?
In how many ways can 8 different colour balls be arranged in a row so that the blue, white, red and green balls are never together?
Find the sum of all the possible numbers of 4 digits formed by digits 4, 5, 5, and 7 using each digit once.
Permutation refers to the arrangement of objects in a definite order. That means permutation is the arrangement of objects in which order matters. The arrangement of r objects out of n objects can be calculated using the permutation formula.
How are permutation problems solved?
Permutation problems are solved using the permutation formula nPr = n!/(n – r)!. The problems include arranging objects in a specific order, forming different words from the letters of a given word, arranging books on a shelf, arranging people in a row, etc.
How many 3-digit even numbers can be made using the digits 1, 2, 3, 4, 6, and 7 if no digit is repeated?
60 three-digit numbers can be made using the given digits.
In how many ways can the letters of the word THOUGHTS be arranged so that the vowels always come together?
The letters of the word THOUGHTS can be arranged in 2520 different ways such that the vowels always come together.
How many numbers are there between 100 and 1000 such that at least one of their digits is 7?
There are 252 numbers between 100 and 1000 such that at least one of their digits is 7.