<p>All five-digit numbers in which each successive digit exceeds its predecessor are arranged in increasing order. The 105th number does not contain the digit</p>
Step-by-Step Solution
Key Concept: Strictly increasing digit sequences correspond to 5-element subsets of {1,...,9}; count cumulatively to find the 105th.
<p>Five-digit numbers with strictly increasing digits are formed by choosing 5 distinct digits from {1,2,...,9} and arranging them in increasing order.</p><p>Total such numbers = \(\binom{9}{5} = 126\).</p><p>Numbers starting with 1: choose 4 from {2,3,...,9} = \(\binom{8}{4} = 70\). Numbers starting with 2: choose 4 from {3,4,...,9} = \(\binom{7}{4} = 35\). Total so far = 105.</p><p>The 105th number is the last number starting with 2, which is 26789. This does not contain digit 1.</p>
Correct Answer: A