# Math. Explain

From the digits 1, 2, 3, and 4, how many positive integers are less than 100,000? Consider the possibilities for 5-digit, 4-digit, 3-digit, 2-digit, and 1-digit numbers and repetition of digits.

1,364
1,024
256

A telephone dial has holes numbered from 0 to 9 inclusive, and eight of these holes are also lettered. How many different telephone numbers are possible with this dial, if each "number" consists of two letters followed by five numbers, where the first number is not zero?

200,000
5,760,000
6,400,000

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1. less than 100,000? highest number can be
44,444 Since three are four possible digits in each of those positions, then
you can have 4^5 choices. 4^5=1024

so ten holes.

two letters, including "O"
26*26*9*10^4

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bobpursley

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