Serial numbers for a product are to be made using 2 letters followed by 2 numbers. If the letters are to be taken from the first 6 letters of the alphabet with no repeats and the numbers are taken from the digits 0 through 9 with no repeats, how many serial numbers can be generated?
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Choose 2 letter out of 6 available =P 6,2
Choose 2 number out of 10 available =P10,2
Using the multiplication principle
=>serial numbers can be generated =P6,2*P10,2
=>6!/(6-2)!*10!/(10-2)!
=>6!/4!*10!/8!
=>6*5*10*9
=>30*90
=>2700
Hence 2700 serial numbers generated"
Choose 2 number out of 10 available =P10,2
Using the multiplication principle
=>serial numbers can be generated =P6,2*P10,2
=>6!/(6-2)!*10!/(10-2)!
=>6!/4!*10!/8!
=>6*5*10*9
=>30*90
=>2700
Hence 2700 serial numbers generated"
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Ok Gennifer--
6 letters, no repeats, 2 letters. = 6C2
10 numbers, no repeats, 2 numbers = 10C2
Now multiply these and you have your answer. 15*45 = 540
6 letters, no repeats, 2 letters. = 6C2
10 numbers, no repeats, 2 numbers = 10C2
Now multiply these and you have your answer. 15*45 = 540
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for first letter you have 6 choice , for 2nd 5 choices, for 3rd digit no. of choice is 10 & for 4th digit choices are 9.
so total no. of serial numbers can be generated = 6×5×10×9 = 2700
so total no. of serial numbers can be generated = 6×5×10×9 = 2700