Question

A passcode can have 5 or 6 digits. Digits can be repeated and leading 0s are allowed. So, 1234 would be a 4 digit code that is different from 01234, which is a 5 digit code. How many different passcodes are possible

Answer 1

Answer:

The number of passcodes possible is 1,100,000

Step-by-step explanation:

Here , we want to calculate the number of different possible passcodes.

For the five digit code,

each number in the code has a possibility of choosing from the digits 0 to 9, so this means that each of the numbers in the code has 10 options.

So for a five digit code, the number of possible choices would be 10 * 10 * 10 * 10 * 10 = 10^5

For a six digit code, the number of possible choice would be 10 * 10 * 10 * 10 * 10 * 10 * 10 = 10^6

So for 5 or 6 digits code, the number of possible choices would be;

10^5 + 10^6 = 10^5(1 + 10)

= 11(10^5) = 1,100,000

Answer 2

The number of passcodes possible is 1,100,000

Calculation of the no of passcode:

For the five-digit code, the no of possible choices should be $10^5$

For the six-digit code, the no of possible choices should be $10^6$

So, the possible choices should be

$10^5 + 10^6 = 10^5(1 + 10)\\\\= 11(10^5)$

= 1,100,000

Hence, The number of passcodes possible is 1,100,000

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