math question

[predentgal]

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A license plate must be made of any 3 digits followed by a letter. How many different license plates are possible if each digit can only be used once and the first digit cannot be 0?

The answer is : 9 x 9 x 8 x 26

I thought it would be 9 x 8 x 7 x 26 since we can't use a any digit more than once and each itme we use a digit we have one less digit, hence 9,8,7. So confused. Can anyone explain?

 

[UCB05]

A license plate must be made of any 3 digits followed by a letter. How many different license plates are possible if each digit can only be used once and the first digit cannot be 0?

The answer is : 9 x 9 x 8 x 26

I thought it would be 9 x 8 x 7 x 26 since we can't use a any digit more than once and each itme we use a digit we have one less digit, hence 9,8,7. So confused. Can anyone explain?

you're almost there. The first number cannot be 0, so you have a range of 1-9 (9 options). Your second number CAN be 0, so you have a range of 0-9, excluding the first number (9 options left). Your third number has a range of 0-9, excluding the two numbers used before (8 options left). Include the 26 letters, and your total is 9 x 9 x 8 x 26.

 

[Frederico Albin]

Well, you cant use any digit more than once... but big thing is this question is the first digit cannot be "0".

So you have 9 digits that can be used for the first digit. For the second, you have 9 digits minus 1 that you used for the first place, but you have to add the "0" now because you can use it, so you are back to 9 digits. Then for the third digit, you do 9-1=8 for the other digit that you used in the second place. So you get 9x9x8x26.

I think the "0" got you confused.

I hope that helps, GL

 

[predentgal]

ooooohhhhh.. You guys are right.. I misread the question.. I thought zero was exluded from all 3 numbers of the license plate.. Thanks for the clarification!!!