Question

For each of the four subsets of the two properties (a) and (b), count the number of four-digit numbers whose digits are either 1,2,3,4, or 5:
(a) The digits are distinct
(b) The number is even

Answer 1

Answer:

– (No restriction) 5 ^4

– (Digits are distinct) 5 × 4 × 3 × 2

– (Even) 5 ^3 × 2. (The last digit has to be 2, but otherwise there is no restriction.)

– (Digits are distinct and even) 2 × 4 × 3 × 2 × 1. (Choose the digits from

right to left.)