Permutations and Factorials in Words

The video tutorial explains how to calculate permutations of letters in words, focusing on factorials and handling repeated letters. It starts with a basic understanding of factorials using the word 'isogram' and progresses to more complex examples like 'cattywampus' and 'artvark', demonstrating how to adjust calculations for repeated letters.

What is an isogram?

• A word with only consonants

• A word with only vowels

• A word without repeated letters

• A word with repeated letters

How many letters are in the word 'isogram'?

• 8

• 7

• 6

• 5

What is the factorial of 7?

• 2,520

• 3,600

• 5,040

• 720

How do you calculate the number of permutations for a word with no repeated letters?

• Use the factorial of the number of letters

• Subtract the number of letters

• Add the number of letters

• Multiply the number of letters

What happens when you switch the positions of two repeated letters in a word?

• A new distinct pattern is created

• The same pattern is maintained

• The word becomes an isogram

• The word becomes longer

In the word 'cattywampus', which letters are repeated?

• T and A

• P and S

• C and W

• Y and M

How do you adjust the permutation calculation for repeated letters?

• Add the factorial of repeated letters

• Subtract the factorial of repeated letters

• Divide by the factorial of repeated letters

• Multiply by the factorial of repeated letters

What is the total number of letters in 'cattywampus'?

• 11

• 10

• 12

• 9

For the word 'artvark', how many times is the letter 'A' repeated?

• Three times

• Twice

• Four times

• Once

What is the factorial expression for the word 'artvark'?

• 8 factorial divided by 2 factorial times 3 factorial

• 8 factorial divided by 2 factorial

• 8 factorial

• 8 factorial divided by 3 factorial