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Serial numbers for a product are to be made using 3 letters followed by 3 digits. The letters are to be taken from the first 5 letters of the alphabet, with no repeats. The digits are taken from the 10 digits 0,1,2,... , 9 with no repeats. How many serial numbers can be generated

Respuesta :

Answer:

43,200 serial numbers can be generated

Step-by-step explanation:

The ordering for the letters and the digits are important. For example, 012 constitutes a different serial number than 210. So we use the permutations formula to solve this question.

Permutations formula:

The number of possible permutations of x elements from a set of n elements is given by the following formula:

[tex]P_{(n,x)} = \frac{n!}{(n-x)!}[/tex]

How many serial numbers can be generated

3 letters, from the first five of the alphabet

3 digits, from a set of 10

So

[tex]T = P_{5,3}*P_{10,3} = \frac{5!}{(5-3)!}*\frac{10!}{(10-3)!} = 43200[/tex]

43,200 serial numbers can be generated

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