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# counting problem

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Each student at State college has a student I.d number consisting of eight digits ( the first digit is nonzero, and digits may be repeated) followed by two of the letters A,B,C,D,and E (letters may not be repeated). How many different student numbers are possible

Mar 28, 2021

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Hey there!

Since the first number cant be zero there are only 9 options (1 thru 9), however for the next seven they can be zero, thus there are 10 options (0 thru 9). for the letters, the first option will be 5 as and the second will be 4 as there is no replacement. This gives:

$$9\times 10^7\times 5\times 4=1800000000$$

Thus there are 1.8billion possible student numbers

I could be wrong here but I do believe this is how you do it... Hope this helped :)

Mar 29, 2021