Answer: 4-digit numbers can be chosen that are even and greater than 3000 is equal to 192.
Step-by-step explanation:
Given data,
4-digit numbers can be chosen that are even and greater than 3000.
For even numbers, each formed 4-digit number must end with 2, 4, or 6. And each such number greater than 3000 must begin with 3, 4, 5, 6, or 7.
Since five digits [1–5] are available, the number may have four or five digits.
All five-digit numbers are greater than 3000, and there are 5! = 120 permutations of the five digits.
Four-digit numbers greater than 3000 must have one of three digits (3 or 4 or 5) as its first digit. The next three digits must be selected from the four remaining digits available, so the number of permutations is: 4 * 3 * 2 = 24.
There are 3 * 24 = 72 numbers of the form 3xxx, 4xxx, 5xxx (all of which are greater than 3000).
The number of possible sequences of [1–5] greater than 3000 include 120 four-digit numbers and 72 five-digit numbers, so the total is 192.
Therefore,
4-digit numbers can be chosen that are even and greater than 3000 is equal to 192.
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