WAEC 2019 · Paper 2 · Q1

(a)
How many even numbers greater than 5000 can be formed using the digits 1, 2, 4, 5, 6 if no digit is used more than once?

Worked solution (try it first)

A five-digit number from these digits is always greater than 5000.
A four-digit one must start with 5 or 6.
Every number must end in 2, 4 or 6.
Four digits starting with 5: 3 choices for the last digit, then $3 \times 2 = 6$ for the middle two: $18$ .
Four digits starting with 6: 2 choices for the last digit (2 or 4), then $3 \times 2 = 6$ : $12$ .
Five digits: 3 choices for the last digit, then $4! = 24$ orders for the rest: $72$ .
Total: $18 + 12 + 72 = 102$ even numbers.