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I am trying to figure out the maximum possible combinations of 10 numbers and 28 letters, with the following form:

$N N N L L L L$

Where $N$ is number and $L$ is letter.

What I think the max maximum possible combinations is but not sure as follow: $28^4$ $*$ $10^3$ $=$ $614,656,000,000,000$

user3188039
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    Well, $28^4\times 10^3$ is correct but you have too many zeroes in the written out form. Just doing it mentally, it must be less than $3^4\times 10^7$ which is much smaller than your number. – lulu Mar 13 '20 at 21:09
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    $28^4 \cdot 10^3 = 614,656,000$ – vonbrand Mar 13 '20 at 21:14
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    Yeah, take off 6 zeros and you have the right answer – Robo300 Mar 13 '20 at 21:14

1 Answers1

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It is just a miscalculation.

There are $10\times10\times10=10^3$ way to choose the three numbers and $28\times28\times28\times28=28^4$ ways to choose the four letters.

Hence, there are $28^4\times10^3=614,656,000$ possible combinations.

Agung Izzul Haq
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