Question

How many different 4-digit PIN codes are there that only include the digits 4, 5, 6, 7, 8 and 9

if each of those digits is only allowed to be used once?

Answer 1

ecall that 6 + 6 + 6 = 6 × 3

Instead of adding 6 three times, you can multiply 6 by 3 and get 18, the same answer.

Similarly,

6 + 6 + 6 + 6 + 6 + 6 + 6 = 6 × 7 = 42

Still by the same token,

2 + 2 + 2 + 2 = 2 × 4

In algebra, 2 × 4 can be written as (2)(4)

You can think of this as four groups of 2.

This situation is shown in the number line below.

You basically start at 0 and count by 2's until you have put four 2's on the number line. You end up at 8 and 8 is positive.

Explanation: