Total number of ways in which all letters of the word GARDEN can be arranged = 6! = 720
There are only two vowels in the word, A and E.
First place A at the first place, E can be occupy any of the remaining 5 places. Total arrangements 5 × 41.
When A in the second place, E can occupy any of 4 places
So Total arrangements 4 × 41.
Repeat this process until A occupies the last but one place. A cannot occupy the last place.
∴ The total number of total arrangement is
(5 + 4 + 3 + 2 + 1) × 41.
15 × 24 = 360
