Arranging Letters in 'Decisions'

The video tutorial explores the arrangement of the word 'decisions' by analyzing its characters, identifying duplicates, and calculating permutations. It covers arranging letters without restrictions, alternating vowels and consonants, and placing vowels first followed by consonants. The tutorial emphasizes understanding patterns and applying factorial calculations to solve arrangement problems.

How many characters are in the word 'decisions'?

• 8

• 7

• 9

• 10

What is the total number of ways to arrange the word 'decisions' without any restrictions?

• 90,720

• 40,320

• 80,640

• 70,560

When arranging 'decisions' with alternating vowels and consonants, which must the sequence start with?

• Vowel

• Consonant

• Either

• Neither

How many vowels are in the word 'decisions'?

• 5

• 4

• 6

• 3

In the arrangement where vowels come first, how many slots are occupied by vowels?

• 3

• 4

• 5

• 6

What is the factorial representation for arranging 5 consonants?

• 6!

• 4!

• 5!

• 3!

In the arrangement where vowels come first, how many consonants follow the vowels?

• 5

• 3

• 4

• 6

What is the main challenge in arranging the word 'decisions' with specific conditions?

• Choosing the first letter

• Meeting the condition

• Avoiding duplicates

• Counting characters

How many pairs of duplicate letters are in the word 'decisions'?

• 4

• 1

• 2

• 3

What is the factorial representation for arranging 4 vowels?

• 4!

• 3!

• 6!

• 5!