The letters of the word "UDAYPUR" are written | vedclass

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Question

(C) The letters of the word "$UDAYPUR$" are $A, D, P, R, U, U, Y$. Total letters = $7$. The letter $U$ repeats $2$ times.Alphabetical order: $A, D, P,

Vedclass · Accepted Answer

$1579$

Vedclass · Answer

(C) The letters of the word "$UDAYPUR$" are $A, D, P, R, U, U, Y$. Total letters = $7$. The letter $U$ repeats $2$ times.Alphabetical order: $A, D, P, R, U, Y$.To find the rank, we count the number of words that come before "$UDAYPUR$":$1$. Words starting with $A$: $\frac{6!}{2!} = 360$$2$. Words starting with $D$: $\frac{6!}{2!} = 360$$3$. Words starting with $P$: $\frac{6!}{2!} = 360$$4$. Words starting with $R$: $\frac{6!}{2!} = 360$$5$. Words starting with $UA$: $5! = 120$$6$. Words starting with $UDAP$: $3! = 6$$7$. Words starting with $UDAR$: $3! = 6$$8$. Words starting with $UDAYP$: $1! = 1$$9$. Words starting with $UDAYR$: $1! = 1$$10$. Words starting with $UDAYU$: $1! = 1$$11$. The next word is "$UDAYPUR$",which is $1$.Total rank = $360 + 360 + 360 + 360 + 120 + 6 + 6 + 1 + 1 + 1 + 1 = 1576$.Therefore, the rank of the word "$UDAYPUR$" is $1577$ (as the word itself is the $1577^{th}$ word).

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:

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