For each question below, calculate the number of four-digit integers (1000 through 9999 inclusive; the first...

For each question below, calculate the number of four-digit integers (1000 through 9999 inclusive; the first digit cannot be 0) that satisfy the specified property:

1) How many four-digit integers are even (for example, 2102 and 8162, but NOT 2001)?

2) How many four-digit integers are consisted of four distinct digits in strictly decreasing order (for example, 9621 and 8742, but NOT 1352)? (Hint: combination problem)

3) How many four-digit integers are consisted of two pairs of distinct digits (for example, 1001 and 2424, but NOT 3333)?

Expert Solution

orchestra answered 2 years ago

For each question below, calculate the number of four-digit integers (1000 through 9999 inclusive; the _rst...

For each question below, calculate the number of four-digit integers (1000 through 9999 inclusive; the _rst digit cannot be 0) that satisfy the specified property: 1. How many four-digit integers are even (for example, 2102 and 8162, but NOT 2001)? 2. How many four-digit integers are consisted of four distinct digits in strictly decreasing order (for example, 9621 and 8742, but NOT 1352)? (Hint: combination problem) 3. How many four-digit integers are consisted of two pairs of distinct digits (for...

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