Permutation Calculator

Permutation is a mathematical concept that refers to the arrangement of elements from a collection, where the order in which the elements are chosen affects the result. In other words, permutation considers different sequences or arrangements of elements as distinct. Permutations are used in various fields such as mathematics, computer science, and statistics for tasks like password generation, event scheduling, and game design.

Explore the following Permutation examples to understand how to calculate arrangements in various scenarios.
Example 1: Forming 3-Digit Numbers

• Problem: How many 3-digit numbers can be formed from the digits 1, 2, 3, 4, and 5 if repetition is not allowed?
• Solution:
  • We need to arrange 3 digits from a set of 5 distinct digits.
  • Use the permutation formula: 5! / (5 - 3)! = 5 x 4 x 3 x 2! / 2! = 60.
• Answer: 60 different 3-digit numbers can be formed.

Example 2: Creating Passwords

• Problem: Create a 4-digit password using digits 0-9 without repeating any digit.
• Solution:
  • We need to arrange 4 digits from a set of 10 distinct digits.
  • Use the permutation formula: 10! / (10 - 4)! = 10 × 9 × 8 × 7 × 6! / 6! = 5040.
• Answer: There are 5040 possible 4-digit passwords.

Example 3: Arranging 2 Flags

• Problem: Given 5 flags of different colours, how many signals can be made using 2 flags in order (one above the other)?
• Solution:
  • We need to arrange 2 flags from a set of 5 distinct flags.
  • Use the permutation formula: 5! / (5 - 2)! = 5 x 4 x 3! / 3! = 20.
• Answer: 20 different signals can be generated.

Engage in this Permutation exercise to explore the concept of permutations through practical questions. Test your ability to calculate arrangements.
Que 1: How many ways can you select and arrange 3 cars out of 5 in a row?
Ans 1: 60.
Que 2: How many ways can you arrange 2 people out of 4 in a row?
Ans 2: 12.
Que 3: In how many ways can you select and arrange 4 digits out of 5 (1, 2, 3, 4, 5) to form a number?
Ans 3: 120.
Que 4: How many ways can you arrange 3 different colored balls out of 6 in a row?
Ans 4: 120.
Que 5: In how many ways can you arrange 5 books out of 7 on a shelf?
Ans 5: 2520.