Five-digit numbers are formed using the digit | vedclass

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Question

(C) The total number of $5$-digit numbers that can be formed using $5$ digits with repetition is $5^5 = 3125$.Since the numbers are arranged in descen

Vedclass · Accepted Answer

$1436$

Vedclass · Answer

(C) The total number of $5$-digit numbers that can be formed using $5$ digits with repetition is $5^5 = 3125$.Since the numbers are arranged in descending order,the serial number of a number $N$ is given by $(Total 	ext{ } numbers 	ext{ } greater 	ext{ } than 	ext{ } N) + 1$.Numbers starting with $7$: $5^4 = 625$.Numbers starting with $5$: $5^4 = 625$.Numbers starting with $37$: $5^3 = 125$.Numbers starting with $357$: $5^2 = 25$.Numbers starting with $355$: $5^2 = 25$.Numbers starting with $3537$: $5^1 = 5$.Numbers starting with $3535$: $5^1 = 5$.Numbers starting with $35337$: $1$ (the number itself).Total numbers greater than or equal to $35337$ is $625 + 625 + 125 + 25 + 25 + 5 + 5 + 1 = 1436$.Thus,the serial number of $35337$ is $1436$.

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 $.........$.

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