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The registration number of the vehicle consists of two letters, three numbers and two letters. How many registration numbers can we form if we use 25 letters.

is this using the combinations theory? or a factorial of 25. I understand that there is only 10 numbers that can be used so maybe 25! x 10!?

harriet
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    It is using common sense, thinking it through, and not grabbing formulas. Most important, it's using the idea that if you can accomplish one task in $a$ different ways, and another task in $b$ different ways, then you can accomplish the pair of tasks in $ab$ different ways. Sometimes called "the multiplication priciple". – Gerry Myerson Mar 05 '19 at 00:53
  • As an aside, $25!\times 10!$ is the number of arrangements of all letters and all digits into a line where the letters all appear at the front and the digits all at the back in some order, for example abcdefghijklmnopqrstuvwxyz0123456789 or hgfedcbazyxwvutsrqponmlkji5847362910 – JMoravitz Mar 05 '19 at 01:05

1 Answers1

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Think about it as placeholders:

$$\underbrace{\_ \space \_ }_\text{letters} |\underbrace{ \_ \space \_ \space \_ }_\text{numbers} |\underbrace{ \_ \space \_ }_\text{letters}$$

I am assuming we can repeat digits and repeat letters, as it isn't stated that we can't.

We are using $25$ letters, and there are $10$ digits (0 through 9)

We start with two letters, so we have $$ 25 \times 25 \times \_ \space \_ \space \_ | \_ \space \_ $$ Once we look at the spots that we want a number, we have $10$ options there, so we plug those in and now have $$ 25 \times 25 \times 10 \times \_ \space \_ | \_ \space \_ $$

See if you can use this to finish the problem.

WaveX
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