All the five-digit numbers in which each succ | vedclass

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Question

(B) five-digit number with strictly increasing digits is uniquely determined by choosing $5$ distinct digits from the set $\{1, 2, 3, 4, 5, 6, 7, 8, 9

Vedclass · Accepted Answer

$5$

Vedclass · Answer

(B) five-digit number with strictly increasing digits is uniquely determined by choosing $5$ distinct digits from the set $\{1, 2, 3, 4, 5, 6, 7, 8, 9\}$. The total number of such integers is $\binom{9}{5} = 126$.$1$. Numbers starting with $1$: We choose $4$ more digits from $\{2, 3, 4, 5, 6, 7, 8, 9\}$. Total = $\binom{8}{4} = 70$.$2$. Numbers starting with $2$: - Starting with $23$: We choose $3$ more digits from $\{4, 5, 6, 7, 8, 9\}$. Total = $\binom{6}{3} = 20$.- Starting with $24$: - Starting with $245$: We choose $2$ more digits from $\{6, 7, 8, 9\}$. Total = $\binom{4}{2} = 6$.- Starting with $246$: - $24678$ ($96^{th}$ number)- $24679$ ($97^{th}$ number)Thus,the $97^{th}$ number is $24679$. This number does not contain the digit $5$.

All the five-digit numbers in which each successive digit exceeds its predecessor are arranged in increasing order of their magnitude. The $97^{th}$ number in the list does not contain the digit:

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