1. ## Basic Statistics

17.) The possible four-digit telephone number extensions that
can be formed if 0, 8, and 9 are excluded as the first digit

In Exercises 21 to 26, use the following experiment. Two digit
numbers are formed, with replacement, from the digits
0–9.

21.) How many two-digit numbers are possible?
25.) How many numbers are greater than 37?

2. ## Re: Basic Statistics

17) For the first digit, now we have only 7 options whereas for each of the rest 3 digits, we have 10 options.
Therefore, all possibilities would be 7x10x10x10 =7,000.

21) All possibilities are 10x10 = 100.

25) Since the largest number could be 99, the answer is 99-37=62.

3. ## Re: Basic Statistics

Originally Posted by zemozamster
17)
21) All possibilities are 10x10 = 100.
all possible pairs are possible and there are 100 of them but all possible pairs is not exactly all 2 digit numbers.

Any pair with 0 as the first digit is excluded so there are only 90 possible 2 digit numbers. These of course are 10-99

4. ## Re: Basic Statistics

Originally Posted by romsek
all possible pairs are possible and there are 100 of them but all possible pairs is not exactly all 2 digit numbers.

Any pair with 0 as the first digit is excluded so there are only 90 possible 2 digit numbers. These of course are 10-99
Why the proceeding 0 needs to be excluded? Why one has to limit into numerical values only? Without clearly saying the application, removing preceding 0 can have a complete different definition (e.g. telephone numbers, postal addresses, personal identity codes).

5. ## Re: Basic Statistics

Originally Posted by zemozamster
Why the proceeding 0 needs to be excluded? Why one has to limit into numerical values only? Without clearly saying the application, removing preceding 0 can have a complete different definition (e.g. telephone numbers, postal addresses, personal identity codes).
Problem 21 states a new experiement and asks "how many two digit numbers are formed". Problem 21 has nothing to do with telephone exchanges.

The two digits "0x", where $x \in 0,1, \dots 9$ do not form a two digit number. They form the 1 digit number $x$