In: Statistics and Probability
Four different digits are chosen from the set {1,2,3,5,6,7} and then arranged to form a four digit number. How many even numbers that are greater than 4000 can be formed?
The first digit can be filled with 3 ways i.e. 5, 6 or 7
The last digit can be filled with 2 ways i.e. 2 or 6.
Even Numbers starting with 5 = 2 * 4 * 3 = 24
Even Numbers starting with 6 = 4 * 3 = 12
Even Numbers starting with 7 = 2 * 4 * 3 = 24
Even numbers that are greater than 4000 can be formed = Even Numbers starting with 5 + Even Numbers starting with 6 + Even Numbers starting with 7
= 24 + 12 + 24
= 60 (ans)