Question

find the total arrangement of word 'ALLAHABAD' such that vowels do not come together?

Answer 1

ALLAHABAD

Vowels: A, A, A, A (Should come together as a single pack)

Consonants: L, L, H, B, D

Step1:

Find starting position for Vowels pack. It could be from positions 1 to 6.

# of ways of selecting starting position for pack of vowels = 6 ways

Step 2:

Rearrangements within pack of vowels = 1 way (All ‘A’ s - so no distinction of order)

Step 3: Arrangement of consonants in remaining 5 positions.

# of ways of doing this = 5!/2! = 60 ways

Total desired combinations = 6 * 1 * 60 = 360 ways

Answer 2

there arr exactly 360 ways and we can find it using the combination method