If all possible numbers are formed by using t | vedclass

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(D) The digits are $S = \{1, 2, 3, 5, 7\}$. Total digits $n = 5$. Numbers are arranged in descending order.$1$. Numbers with $5$ digits: $5! = 120$.$2

Vedclass · Accepted Answer

$271$

Vedclass · Answer

(D) The digits are $S = \{1, 2, 3, 5, 7\}$. Total digits $n = 5$. Numbers are arranged in descending order.$1$. Numbers with $5$ digits: $5! = 120$.$2$. Numbers with $4$ digits: $^5P_4 = 120$.$3$. Numbers with $3$ digits starting with $7$: $^4P_2 = 12$.$4$. Numbers with $3$ digits starting with $5$: $^4P_2 = 12$.$5$. Numbers with $3$ digits starting with $37$: $^3P_1 = 3$.$6$. Numbers with $3$ digits starting with $35$: $^3P_1 = 3$.$7$. Numbers with $3$ digits starting with $32$: The remaining digits are $\{1, 5, 7\}$. In descending order,these are $327, 325, 321$. The number $327$ is the first in this sequence.Rank $= 120 + 120 + 12 + 12 + 3 + 3 + 1 = 271$.

If all possible numbers are formed by using the digits $1, 2, 3, 5, 7$ without repetition and they are arranged in descending order,then the rank of the number $327$ is

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