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

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Question

(B) 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

$1578$

Vedclass · Answer

(B) 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: $A, D, P, R, U, Y$.Words starting with:$A$: $\frac{6!}{2!} = 360$$D$: $\frac{6!}{2!} = 360$$P$: $\frac{6!}{2!} = 360$$R$: $\frac{6!}{2!} = 360$$UA$: $5! = 120$$UDAP$: $3! = 6$$UDAR$: $3! = 6$$UDAYP$: $1! = 1$$UDAYR$: $1! = 1$$UDAYU$: $1! = 1$$UDAYPUR$: $1$Summing these: $360 + 360 + 360 + 360 + 120 + 6 + 6 + 1 + 1 + 1 + 1 = 1577 + 1 = 1578$.Wait,let us re-calculate carefully:Words starting with $A, D, P, R$ are $4 	imes 360 = 1440$.Words starting with $UA$ are $120$.Words starting with $UDAP$ are $3! = 6$.Words starting with $UDAR$ are $3! = 6$.Words starting with $UDAYP$ are $1! = 1$.Words starting with $UDAYR$ are $1! = 1$.Words starting with $UDAYU$ are $1! = 1$.Next is $UDAYPUR$ which is $1$.Total rank = $1440 + 120 + 6 + 6 + 1 + 1 + 1 + 1 = 1576$.

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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