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# help with counting

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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

Jul 31, 2020

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This involves casework. So, let's first see how many options there are for 5 digits:

This is basically 10 to the power of 5 (ten numbers from 0-9, and you can repeat, so 10(10)(10)(10)(10), which is 10^5), which is 100,000

(If you don't understand combinations, here is a link you could refer to: https://www.mathsisfun.com/combinatorics/combinations-permutations.html)

Same thing for 6, but 10^6, and you would get 1,000,000. Add those together, and you have 1,100,000.

(Not sure if you acctually read my explanation, or read this , but here is a trickier practice problem for you (refer to website linked above if confused). Use the same problem that you stated above, BUT, instead, you can't repeat digits. (maybe not that much trickier, but you should try it.))

Jul 31, 2020