Hello, BabyMilo

There are: . possible 4-digit numbers.A 4-digit number is to be made by choosing four different digits from the set {1,2,3,4,5,6,7}.

Find the probability that the number is even and greater than 6000.

How many of them are even and greater than 6000?

There are two cases to consider.

[1] The number begins with "6": .6 _ _ _

We have: .{1, 2, 3, 4, 5, 7} to work with.

The last digit must be even: 2 choices.

The middle two digits are selected from the remaining 5 digits: . choices.

Hence, there are: . even numbers that begin with "6".

[2] The number begins with "7": .7 _ _ _

We have: .{1, 2, 3, 4, 5, 6} to work with.

The last digit must be even: 3 choices.

The middle two digits are selected from the remaining 5 digits: . choices.

Hence, there are: . even numbers that begin with "7".

Then there are: . even numbers greater than 6000.

Therefore: .