Question

Zara has forgotten her 4-digit PIN code.

She knows the first digit is a factor of 10 and the 4 digits make a number divisible by 5.
How many different sets of 4 digits could it be?

Answer 1

800 different 4 digit passwords can be the pin

Explanation:

Since the first digit is a factor of 20, the factors of 20 are 1,2,4,5,10,20. We only need the single digit factors which are 1,2,4 and 5.

These 4 numbers can be permuted in 1 way for the first digit, so we have ⁴P₁.

For the second digit, we have 10 digits permuted in 1 way, ¹⁰P₁ and also for the third digit, we have

10 digits permuted in 1 way, and for the last digit, which is divisible by 5, it is either a 0 or 5, so we have two digits permuted in 1 way,

So, the number of different 4 digit number that Zara'2 4-digit PIN code could be is

4 × 10 × 10 × 2 = 800 different sets of digits

Answer 2

800 different sets of digits


Since the first digit is a factor of 20, the factors of 20 are 1,2,4,5,10,20. We only need the single digit factors which are 1,2,4 and 5. These 4 numbers can be permuted in 1 way for the first digit, so we have ⁴P₁.
For the second digit, we have 10 digits permuted in 1 way, ¹⁰P₁ and also for the third digit, we have 10 digits permuted in 1 way, ¹⁰P₁ and for the last digit, which is divisible by 5, it is either a 0 or 5, so we have two digits permuted in 1 way, ²P₁.
So, the number of different 4 digit number that Zara'2 4-digit PIN code could be is ⁴P₁ × ¹⁰P₁ × ¹⁰P₁ × ²P₁ = 4 × 10 × 10 × 2 = 800 different sets of digits