Question

You need to create a 4-digit PIN for your Visa Debit card. a. How many PINs are possible if the first digit must be a 5 and repetition is NOT allowed? b. How many PINs are possible if the first digit must be a 5 and repetition of consecutive digits is NOT allowed? (So for example, a PIN of 5757 or 5785 would be allowed, but a code of 5578 or 5778 or 5788 would NOT be allowed.)

Answer 1

a) 504 possible

b) 729 possible

Explanation:

Given data

first digit = 5

to find out

How many PINs are possible

solution

we know that we have 0 to 9 digit

in 1st part we know first digit is 5

so remaining is 3 digit and repetition is NOT allowed

so in 2nd position we have 9 chance

in 3rd position we have left 8 chance because first 2 position fill and repetition is not allow

so in 4th position we have 7 chance

so that we have 9 × 8 × 7 = 504 chance

in 2nd part

we have 5 is fix in first position

in 2nd position we have 10 chance but 5 is fix in first and no consecutive repetition allow so 9 chance is left

in 3rd position again same reason we have 9 chance

in 4th position we have 9 chance

so remaining we have 9 × 9 × 9 = 729 chance