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# Combinatorics and Permutations

Created by
@UnfetteredChiasmus7291

## Questions and Answers

### How many permutations can be made out of the letters in the word ISLAND taking four letters at a time?

• 720
• 24
• 120
• 360 (correct)
• ### How many 4 digit numbers can be formed without repeating any digit, from the digits 1, 2, 3, 4 and 6?

• 120 (correct)
• 150
• 140
• 130
• ### How many permutations can be made out of the letters of the word ENGINEERING?

• 277,200 (correct)
• 55,440
• 39,916,800
• 3,326,400
• ### How many ways can 3 men and 4 women be seated on a bench if the women are to be together?

<p>720</p> Signup and view all the answers

### In how many ways can 5 people line up to pay their electric bills?

<p>120</p> Signup and view all the answers

### How many ways can 7 people be seated at a round table?

<p>720</p> Signup and view all the answers

## Study Notes

### Permutations and Combinations

• Permutations of 4 letters from the word ISLAND can be made in 360 ways.
• 4 digit numbers can be formed without repeating any digit from the digits 1, 2, 3, 4, and 6 in 120 ways.
• Permutations of letters in the word ENGINEERING can be made in 277,200 ways.

### Seating Arrangements

• 3 men and 4 women can be seated on a bench where women are together in 720 ways.
• 5 people can line up to pay their electric bills in 120 ways.
• 5 people can line up to pay their electric bills where two particular persons refuse to follow each other in 60 ways.

### Circular Arrangements

• 7 people can be seated at a round table in 360 ways.

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## Description

Practice problems on permutations and combinations, including seating arrangements and forming numbers. Calculate the number of ways to arrange objects in different scenarios.

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