Answer to Question #119516 in Combinatorics | Number Theory for Hussain Ousman Darboe

Question

How many even numbers greater than 5000 are there using digits {1,3,4,5,67}

Answer 1

We have total six numbers {1,3,4,5,6,7} which we have to used to form number. First digit of number greater than 5000, will be from 5,6,7. So, for first digit three cases are possible. For even number last digit have two choices either it be 4 or 6.

So, total cases of even numbers greater than 5000

= (1st digit choice) $\times$ (last digit choice) $\times$ (2nd, 3rd, 4th, 5th digit choice)

= $3\times 2 \times 6^4 = 6^5$.