Permutation and CombinationMedium
Question
The letters of the word "UDAYPUR" are written in all possible ways with or without meaning and these words are arranged as in a dictionary. The rank of the word "UDAYPUR" is :
Options
A.1580
B.1578
C.1579
D.1581
Solution
ADIPRUU
$$\begin{matrix} & A \rightarrow \frac{6!}{2!} = 360 \\ & D \rightarrow \frac{6!}{2!} = 360 \\ & P \rightarrow \frac{6!}{2!} = 360 \\ & R \rightarrow \frac{6!}{2!} = 360 \\ & UA \rightarrow 5! = 120 \\ & UDAP \rightarrow 3! = 6 \\ & UDAR \rightarrow 3! = 6 \\ & UDAU \rightarrow 3! = 6 \\ & UDAYPRU \rightarrow 1 \\ & UDAYPUR \rightarrow 1 \\ & Total = 1580 \end{matrix}$$
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