All the letters of the word GTWENTY are writt | vedclass

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Question

(B) The letters in the word $GTWENTY$ are $G, T, W, E, N, T, Y$. Total letters = $7$. The frequency of letters is: $T$ appears $2$ times,others appear

Vedclass · Accepted Answer

$553$

Vedclass · Answer

(B) The letters in the word $GTWENTY$ are $G, T, W, E, N, T, Y$. Total letters = $7$. The frequency of letters is: $T$ appears $2$ times,others appear $1$ time.First,arrange the letters in alphabetical order: $E, G, N, T, T, W, Y$.$1$. Words starting with $E$: The remaining $6$ letters $(G, N, T, T, W, Y)$ can be arranged in $\frac{6!}{2!} = \frac{720}{2} = 360$ ways.$2$. Words starting with $G$:- $GE$: Remaining $5$ letters $(N, T, T, W, Y)$ can be arranged in $\frac{5!}{2!} = \frac{120}{2} = 60$ ways.- $GN$: Remaining $5$ letters $(E, T, T, W, Y)$ can be arranged in $\frac{5!}{2!} = 60$ ways.- $GT$:- $GTE$: Remaining $4$ letters $(N, T, W, Y)$ can be arranged in $4! = 24$ ways.- $GTN$: Remaining $4$ letters $(E, T, W, Y)$ can be arranged in $4! = 24$ ways.- $GTT$: Remaining $4$ letters $(E, N, W, Y)$ can be arranged in $4! = 24$ ways.- $GTW$:- $GTWE$: Remaining $3$ letters $(N, T, Y)$ can be arranged in $3! = 6$ ways.- $GTWN$: Remaining $3$ letters $(E, T, Y)$ can be arranged in $3! = 6$ ways.- $GTWT$: Remaining $3$ letters $(E, N, Y)$ can be arranged in $3! = 6$ ways.- $GTWY$: Remaining $3$ letters $(E, N, T)$ can be arranged in $3! = 6$ ways.- $GTWE...$ (Wait,the word is $GTWENTY$):- $GTWE$: $N, T, Y$ (Remaining $3$ letters) $\rightarrow 3! = 6$ ways.- $GTWEN$: $T, Y$ (Remaining $2$ letters) $\rightarrow 2! = 2$ ways.- $GTWENT$: $Y$ (Remaining $1$ letter) $\rightarrow 1! = 1$ way.- $GTWENTY$: $1$ way.Summing up: $360 + 60 + 60 + 24 + 24 + 24 + 1 = 553$.

All the letters of the word $GTWENTY$ are written in all possible ways with or without meaning and these words are written as in a dictionary. The serial number of the word $GTWENTY$ is:

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