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Determine the number of possible serial numbers that can be formed with the following restrictions: The first two spaces must be consonants, the next three are non-zero numbers, and the last space is a vowel.

User Ither
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1 Answer

3 votes

Step-by-step explanation

We have a total of 26 in the standard alphabet, 5 of them are vowel and the remaining 21 are consonants.

Also, we have 9 non-zero numbers.

The restrictions don't mention that we can't repeat letters or numbers, so we will assume we can repeat.

Since the first 2 spaces are consonants, we can pick each of them from 21 possibilities, so the combinations for that part are:


21\cdot21

The next three are the non-zero numbers, so we can pick each from 9 possibilities:


21\cdot21\cdot9\cdot9\cdot9

And the last is a vowel, so we can only pick from the 5 possibilities, so we have:


21\cdot21\cdot9\cdot9\cdot9\cdot5

These are all the possibilities, so we just need to evaluate the product:


21\cdot21\cdot9\cdot9\cdot9\cdot5=1,607,445

Answer

So, there are 1,607,445 possibilities.

User Mankeomorakort
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