Zara has forgotten her 4-digit PIN code. She knows the first digit is a factor of 20 and the 4 digits make a number divisible by 5. How many different sets of 4 digits could it be?

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

Palky Palky · Answer 2 · 2022-01-20T09:00:30+01:00

800 different sets of 4 digit PIN could be made.

The First (single) digit is a factor of 20. So, it is among 1, 2, 4, 5. The other factors 10 & 20 are ignored, as they are 2 digits.

So, ways of choosing 1 out of 4 digits = 4 P 1 = 4

The Second digit can be any digit among he 10 digits : 0, 1, 2, 3, 4, 5, 6, 7, 8, 9

So, ways of choosing 1 out of 10 digits = 10 P 1 = 10

Third digit can also be any digit among he 10 digits : 0, 1, 2, 3, 4, 5, 6, 7, 8, 9

So, ways of choosing 1 out of 10 digits = 10 P 1 = 10

The Fourth digit can be amongst only 0 & 1, as the final PIN is divisible by 5.

So, ways of choosing 1 out of 2 digits = 2 P 1 = 2

Hence, total number of ways = 4 x 10 x 10 x 2 = 800 ways

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