Question

The letters of the word $AEIOU$ are permuted in all possible ways and the words thus formed are arranged as in a dictionary, the rank of the word $UIOEA$ is:

• A. $118$
• B. $116$
• C. $114$
• D. $120$

Answer 1

The correct option is C $114$

A_ _ _ _
Implies $4!$ ...(i)
E _ _ _ _
Implies $4!$ ...(ii)
I _ _ _ _
Implies $4!$
O _ _ _ _
Implies $4!$ ...(iii)
U A _ _ _
Implies $3!$ ...(iv)
U E _ _ _
Implies $3!$ ...(v)
U I A _ _
Implies $2!$ ...(vi)
U I E _ _
Implies $2!$ ...(vii)

The next numbers will be $UIOAE$ and $UIOEA$
Hence the rank of the given word will be
$=4(4!)+2(3!)+2(2!)+2$
$=96+12+4+2$
$=114$