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How many three digit even numbers are possible if the left digit cannot be zero?
450
How many seven-digit telephone numbers are possible if the first two digits cannot be ones or zeros?
That makes:* 8 options for the first digit * 8 options for second digit * 10 options for the third digit * ... etc. Just multiply all the numbers together.
How many possible 3 digit area codes can be created without repeating a number?
The number of 3-digit numbers with no repeated digits is simply 10x9x8 = 720, if you allow, for example, 012 as a 3-digit number. There are 10 digits, any of which might be the first digit. The second digit can be any digit except the digit that was used for the first digit, leaving 9 possibilities. The third digit then has 8 possibilities, since it can't be the same as the first or second digit. The actual number of possible area codes will be lower, because there are additional restrictions on the number combinations for a valid area code. For example, in North America (USA, Canada, etc.), the first digit of an area code cannot be 0 or 1 and the middle digit cannot be 9.
How many possible combinations can you make out of a 5 digit alpha numeric numbers?
90
How many different 7 digit phone numbers are possible if the first digit cannot be 0 or 1?
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