Calculator Book Serial numbers for a product are to be made using 4 letters foll

Question

Calculator Book Serial numbers for a product are to be made using 4 letters followed by 4 numbers. If the letters are to be taken from the first 5 letters of the alphabet with no repeats and the numbers are taken from the digits 0 through 9 with repeats possible, how many serial numbers can be generated? (If necessary, consult a list of formulas) Clear Undo Help Next>> Explain https/www-awh.aleks.com/alekscgi/w/isl.exe/1o u-lgNestker7j8p3jH-h-6bjbonmD3q19041MT6bkoi-COIXAWIMMEdBAMWRSts Type here

Explanation / Answer

We know that,

nPr = (n!)/(n-r)!

Serial numbers for a product are to be made using 4 letters followed by 4 numbers.

If the letters are to be taken from the first 5 letters of the alphabet with no repeats, then,

the arrangements of letter= 5P1* 4P1* 3P1* 2P1

= 5*4*3*2

= 120

and the numbers are taken from the digits 0 through 9 (n=10) with repeats possible   

the arrangements of digits= 10P1* 10P1* 10P1* 10P1

= 10*10*10*10

= 10000

Thus, total serial numbers for a product are to be made using 4 letters followed by 4 numbers can be generated

= (total arrangement of numbers)*(total arrangement of letters)

= 10000*120

= 1200000

Hence, total serial numbers for a product are to be made using 4 letters followed by 4 numbers can be generated is 1200000.

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