Question 198047: The numbers 0 through 9 are used in code groups of four to identify an item of clothing. Code 1083 might identify a blue blouse, size medium. The code group 2031 might identify a pair of pants, size 18, and so on. Repetitions of numbers are not permitted, i.e., the same number cannot be used more than once in a total sequence. As examples, 2256, 2562 or 5559 would not be permitted. How many different code groups can be designed?
Found 2 solutions by solver91311, stanbon:
Answer by solver91311(24713)   (Show Source):
You can put this solution on YOUR website!
There are 10 ways ( 0 through 9 ) to select the first number. Once the first number has been selected there remain 9 ways to select the second number because of the restriction on repetition of digits. Then 8 ways for the third number and 7 ways for the fourth number, hence:
You can do your own arithmetic.
John
Answer by stanbon(75887)  (Show Source):
You can put this solution on YOUR website! The numbers 0 through 9 are used in code groups of four to identify an item of clothing. Code 1083 might identify a blue blouse, size medium. The code group 2031 might identify a pair of pants, size 18, and so on. Repetitions of numbers are not permitted, i.e., the same number cannot be used more than once in a total sequence. As examples, 2256, 2562 or 5559 would not be permitted. How many different code groups can be designed?
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# of sets of 4 digits is 10C4 = 210
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# of arrangements of each set of 4 is 4!= 24
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Ans: # of code numbers is 24*210 = 5040
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Cheers,
Stan H.
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