Binomial Theorem Question Help
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Binomial Theorem Question Help

[From: ] [author: ] [Date: 11-12-22] [Hit: ]
ans: 5,539,......
A homework question that I am having trouble finishing

A license plate consists of 3 letters followed by three numbers. The letters are not allowed to repeat. The numbers may repeat. The letter o and the number zero may not appear on the same license plate. How many different license plates are possible?

I know the left side is 26x25x24 and the right side is 10x10x10 which would give you 15,600,000 combinations, but that is only if you CAN include the zero and the o and you CANNOT. Anyone have any suggestions. Help is greatly appreciated!!

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26x25x24 = 15,600 letter combinations. Of those, 25x24x23 = 13800 do not use O, and the remaining 1800 use the letter O at least once.

Filling in the last three numbers, you end up with (13800)*(10*10*10) + 1800*(9*9*9) possible combinations.

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the q doesn't say that 0 or o can't appear.
it only says that 0 & o can't both appear on the same license plate
total # of license plates : 26*25*24*10*10*10
minus # of license plates with neither o nor 0 : 25*24*23*9*9*9
ans: 5,539,800
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