$32 \cdot 18$ A positive integer like 34689 is called an "ascending number," where each digit is greater than the digit to its immediate left. There are $C_{9}^{5}\binom{9}{5}=126$ five-digit "ascending numbers." If these numbers are arranged in ascending order, the 97th "ascending number" will not contain the digit
(A) 4.
(B) 5.
(C) 6.
(D) 7.
(E) 8.
(48th American High School Mathematics Examination, 1997)
［Solution］The five-digit "ascending digit numbers" starting with 1,2 are as follows:
$1 * * * *$ type has $C_{8}^{4}=70$;
$23 * * *$ type has $C_{6}^{3}=20$;
$245 * *$ type has $C_{4}^{2}=6$.

In total, there are $70+20+6=96$.
Thus, the 97th "ascending digit number" is 24678, which does not contain 5.
Therefore, the answer is $(B)$.