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Solution


Q.

Five digit numbers are formed using the digits 1, 2, 3, 5, 7 with repetitions and are written in descending order with serial numbers. For example, the number 77777 has serial number 1. Then the serial number of 35337 is _______ .             [2023]

Ans.

(1436)

Number of 5-digit numbers starting with digit 1 =5×5×5×5=625

No. of 5-digit numbers starting with digit 2 =54=625

No. of 5-digit numbers starting with 31 =5×5×5=125

No. of 5-digit numbers starting with 32 =5×5×5=125

No. of 5-digit numbers starting with 33 =5×5×5=125

No. of 5-digit numbers starting with 351 =5×5=25

No. of 5-digit numbers starting with 352 =5×5=25

No. of 5-digit numbers starting with 3531 =5

No. of 5-digit numbers starting with 3532 =5

Before 35337, there will be 4 numbers, so the rank of 35337 will be 1690.

So, in descending order serial number will be, 3125-1690+1=1436