Permutation and Combination with examples (Part-1)
The permutation means ‘ordered selection’. It can be defined as the number of ways ‘r’ things can be selected and arranged, from amongst ’n’ different things, at a time.
Here nPr represents the possible number of ways r things can be selected and arranged, from n different things. (n ≥ r)
The Combination deals with the possible number of ways ‘r’ things can be selected out of ’n’ different things. Here the order is not important. It is represented by nCr.
Real-life examples of Permutations and Combinations
Permutations deal with the arrangement of items so the Order of things is important.
Example: The combination lock can’t be unlocked until the right sequence of digits or alphabets (Password) is not entered. In Combination, Order of the things is not important. Like the selection of 11 team members out of 20.
Difference between permutations and Combinations
How many arrangements/groups of two letters can be formed using the letters A, B, and C?
Arrangements mean Permutations.
Groups mean Combinations.
Counting Principle
Before using formulas we have to know the concept behind these formulas which is known as the Counting Principle.
Consider choice A has ‘m’ options and choice B has ’n’ options. Now the total number of ways to choose one option from A and then one option from B would be m×n.
Arrangement of digits
Que 1: How many three-digit numbers can be formed with the digit 1,2,3,4,5?
Case 1: The repetition of digits is allowed.
Here we have three vacant places, where digits have to be placed according to given conditions.
Hundreds place: 5 choices
Tens place: 5 choices
Unit place: 5 choices
Total possible numbers (arrangements)= 5×5×5= 125
Case 2: The repetition of digits is not allowed.
Hundreds place: 5 choices
Tens place: 4 choices (One digit is already in use)
Unit place: 3 choices (Two digits are already in use)
Total possible numbers (arrangements) = 5×4×3= 60
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