Question

How many even integers are there between 2,000 and 7,000 whose digits are all different and come from the set {1, 2, 3, 5, 7, 8, 9}?

Answer 1

There are 840 even integers between 2,000 and 7,000 whose digits are all different and come from the set {1, 2, 3, 5, 7, 8, 9}.

Step-by-step explanation:

To find the number of even integers between 2,000 and 7,000 whose digits are all different and come from the set {1, 2, 3, 5, 7, 8, 9}, we need to consider the possible options for each digit.

For the first digit, it can be any of the seven options {2, 3, 5, 7, 8, 9}.

For the second digit, it can be any of the six remaining options.

For the third digit, it can be any of the five remaining options.

And so on. Continuing this pattern, we find that there are a total of 7 × 6 × 5 × 4 = 840 even integers between 2,000 and 7,000 that satisfy the given conditions.