Correct Answer - Option 3 : 2160
Given:
The word is "GEOMETRY"
Concept Used:
n! = n(n - 1)(n - 2) ......3.2.1
Where,
n = positive integer
Calculation:
According to the question, we have
The total number of letters = G, E, O, M, E, T, R, Y
⇒ 8
Total vowels = E, O, E
⇒ 3
When all vowels come together,
The total letters will be = G, M, T, R, Y, (EOE)
⇒ 6
The total repeated letters = E, E
⇒ 2
Now,
Required number of ways = (6! × 3!)/(2!)
⇒ {6 × 5 × 4 × 3 × 2 × 1 × (3 × 2 × 1)}/(2 × 1)
⇒ 2160
∴ The 2160 word can be formed of the word "GEOMETRY" when vowels are always come together.
