Mathematics - Permutation & Combination Question with Solution | TestHub

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

$3125-1690+1=1436$