A four 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 no. is even and greater than 6000.
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: .