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If two digits are missing, only one digit is used, resulting in all digits being the same. There are 3 such integers (11111, 44444, 55555).
Using the principle of inclusion-exclusion, the number of integers where at least one digit is missing is:
- 3 = 93
Thus, the number of 5-digit integers where each digit appears at least once is:
- 93 = 150
Therefore, the final answer is:
\boxed{150}
Question:
In a circular arrangement, 5 scientists and 4 engineers are seated around a table. If all scientists must sit together, in how many distinct ways can they be seated?
First, treat the group of 5 scientists as a single "block." In a circular arrangement, the number of distinct ways to arrange \( n \) objects is \((n-1)!\). Here, we have the "block" of scientists and 4 engineers, making 5 objects in total: