Five digit numbers are formed using the digits 1, 2, 3, 5, 7 with...

Given,

Five digit numbers are formed using the digits $1, 2, 3, 5, 7$ with repetitions and are written in descending order with serial numbers,

Now number of $5$ digit numbers starting with digit $1$ will be $= 5 \times 5 \times 5 \times 5 = 625$

Number of $5$ digit numbers starting with digit $2$ will be $= 5 \times 5 \times 5 \times 5 = 625$

Number of $5$ digit numbers starting with digit $31$ will be $= 5 \times 5 \times 5 = 125$

Number of $5$ digit numbers starting with digit $32$ will be $= 5 \times 5 \times 5 = 125$

Number of $5$ digit numbers starting with digit $33$ will be $= 5 \times 5 = 25$

Number of $5$ digit numbers starting with digit $351$ will be$= 5 \times 5 = 25$

Number of $5$ digit numbers starting with digit $352$ will be $= 5 \times 5 = 25$

Number of $5$ digit numbers starting with digit $3531$ will be $= 5$

And number of $5$ digit numbers starting with digit $3532$ will be $= 5$

And before $35337$ will be $4$ numbers, So rank of $35337$ will be $1690$

So, in descending order serial number will be

$3125 - 1690 + 1 = 1436$