AIEEE 2004 (Offline)Question 1
How many ways are there to arrange the letters in the word GARDEN with vowels in alphabetical order
Permutation and Combination
Solution
Concept. Of the $2!$ orders of A and E, only A before E is allowed, so divide by $2!$. Formulas used. (1) $r$ items in a fixed order among $n$: $\frac{n!}{r!}$Step 1 - All arrangements. GARDEN has $6$ different letters: $6!=720$. Step 2 - Vowels A, E in order. Half of them: $\frac{720}{2}=360$. Answer: C