Numbers between 1 and 10,000 are formed using | vedclass

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(A) The digits available are ${2, 3, 4, 4}$.$1.$ One-digit numbers: ${2, 3, 4}$. Total = $3$.$2.$ Two-digit numbers: Using ${2, 3, 4, 4}$,the possible

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$17$

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(A) The digits available are ${2, 3, 4, 4}$.$1.$ One-digit numbers: ${2, 3, 4}$. Total = $3$.$2.$ Two-digit numbers: Using ${2, 3, 4, 4}$,the possible numbers are ${23, 24, 32, 34, 42, 43, 44}$. Total = $7$.$3.$ Three-digit numbers: Using ${2, 3, 4, 4}$,the possible numbers are ${234, 243, 244, 324, 342, 344, 423, 424, 432, 434, 442, 443}$. Total = $12$.$4.$ Four-digit numbers: The rank of $324$ is $3 + 7 + (	ext{numbers starting with } 2 	ext{ or } 3 	ext{ before } 324)$.Numbers starting with $2$: ${2344, 2434, 2443}$ ($3$ numbers).Numbers starting with $3$: ${3244, 3424, 3442}$ ($3$ numbers).Rank of $324 = 3 + 7 + 3 + 1 = 14$.$5.$ Rank of $4324$: Numbers with $1, 2, 3$ digits = $3 + 7 + 12 = 22$.Numbers starting with $2$: $3$ permutations of ${3, 4, 4} = 3$.Numbers starting with $3$: $3$ permutations of ${2, 4, 4} = 3$.Numbers starting with $42$: $2$ permutations of ${3, 4} = 2$.Numbers starting with $4324$: $1$.Rank of $4324 = 22 + 3 + 3 + 2 + 1 = 31$.Therefore,$x - y = 31 - 14 = 17$.

Numbers between $1$ and $10,000$ are formed using the digits $2$ and $3$ exactly once and the digit $4$ twice. If the numbers thus formed are arranged in increasing order and $x, y$ represent the ranks of $4324$ and $324$ respectively,then $x-y=$

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