WAEC Further Mathematics 2018 Paper

Concept:Numbers formed from the digits $1,2,3,4,5$ without repetition can have 3, 4, or 5 digits. Any 4-digit or 5-digit number is automatically greater than 150.Explanation:Total 4-digit numbers formed = ${}^5P_4 = 5 \times 4 \times 3 \times 2 = 120$.Total 5-digit numbers formed = ${}^5P_5 = 5! = 120$.So, numbers greater than 150 from these lengths = $120 + 120 = 240$.Now count 3-digit numbers greater than 150.Total 3-digit numbers without repetition = ${}^5P_3 = 5 \times 4 \times 3 = 60$.The 3-digit numbers not greater than 150 must start with 1, and the second digit must be 2, 3, or 4.These are: $123, 124, 125, 132, 134, 135, 142, 143, 145$, which are exactly 9 numbers.Thus, valid 3-digit numbers = $60 - 9 = 51$.Total valid numbers = $240 + 51 = 291$.Answer:The number of numbers greater than 150 is $291$, which corresponds to option C.