Quandaries and Queries
 


how many 3 digit combinations can be made with 0-9. i have been told only 1,000. when i asked jeeves the response was 750 without using any digit twice. i have entered a raffle and received a ticket with 4 sets of 3 digit numbers. they are selling 250 tickets and are telling me that all combinations are covered with 250 raffle tickets with 4 sets of 3 digit numbers. they are using a daily lottery game to determine the winner. i feel there is more than 1000 combinations as numbers can come up twice in a drawing

thank you
kevin



Hi Kevin,

Think about forming one of the three digit numbers. If the digits are allowed to repeat then you can choose any of the ten digits as the first digit, and once that is chosen you can choose any of the ten digits for the second digit, and again once the first two are chosen you can choose any of the ten digits as the final digit. Thus the number of ways you can form the three digit number is

10 10 10 = 1000.

If the digits cannot repeat then, again you can choose any of the ten digits for the first digit, but once that is chosen you can only chose the second digit from the nine remaining, and once the first two are chosen you can choose the final digit from the eight remaining. Thus the number of ways you can form the three digit number is

10 9 8 = 720.

Penny


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