Question

Given the digits 0, 1, 2, 3, 4 and 5.

(a) How many five-digit numbers can be formed?

(b) How many of the five-digit numbers ending with zero?

(c) How many of the five-digit numbers with the odd digits in odd places?

Answer 1

(a) Five-digit numbers (number of) = 5(5!) = 600

(b) Number of numbers ending with zero = ⁵P₄ = 120

(c) The 3 odd numbers may form the 3 odd places in 3! ways and the 3 even numbers may form the two even places in 3! ways. Thus, the total number of number is 3! 3! = 36.