Respuesta :
Ok guys, let me explain in a way you can understand.
let’s say there’s 7 blanks :
_ _ _ _ _ _ _
the first can’t be 0 or 1 so that means that it can be 2,3,4,5,6,7,8,9 which is 8 numbers
Now we have settle what the first digit can or can’t be, there are 6 numbers left.
Because there are no more restrictions for phone numbers that don’t work (first digit can’t be one or zero was the only restriction), the question then becomes : How many 6 digit numbers are possible (000000) can count , well we know that the biggest 6 digit number is 999999 and the smallest is 000000. That means there are 999999–000000+1 numbers between them inclusive. For those of you that are curious how I got the plus one, when you are counting the amount of numbers between let’s say a and b inclusive, the amount of numbers between them inclusive is |a-b| +1. Example : The amount of numbers between 2 and 13 inclusive is just |2–13|+1 which is 12. 2,3,4,5,6,7,8,9,10,11,12,13 is 12 numbers so |a-b|+1 works for the amount of numbers between a and b inclusive.
Anyways, back to the problem. 999999–000000+1 means there are 1000000 or 1 million possible 6 digit numbers. But that’s not the answer to the problem because each 1 of those 1 million 6 digit numbers needs a 7th digit which and be any number from 2–8 . This means that you need to multiply 1000000 by 8 to get 8 million possible phone numbers. If your wondering why I multiplied by 8, let’s say the number abcdef is one of the possible 6 digit numbers. If you add a 7th digit 2–9 to our number abcdef, then our number abcdef can be 2abcdef, 3abcdef, 4abcdef, 5abcdef, 6abcdef, 7abcdef, 8abcdef, 9abcdef.
Just a quick side note for any misconceptions, when I say the number abcdef, I don’t mean a times b times c times d times e times f, I mean a is the number in the hundred thousands place, b is the number in the 10 thousands place, c is the number in the thousands place, d is the number in the hundreds place, e is the number in the tens place, f is the number in the ones place.
Back to the problem, because there are 8 possible numbers for the 7th digit (AKA the first number in the phone number) you need to multiply the 1000000 different 6 numbers by 8 because each of those numbers has 8 variations.
In summary, there are 8*1000000 or 8 million different phone numbers whose digits aren’t 0 or 1
let’s say there’s 7 blanks :
_ _ _ _ _ _ _
the first can’t be 0 or 1 so that means that it can be 2,3,4,5,6,7,8,9 which is 8 numbers
Now we have settle what the first digit can or can’t be, there are 6 numbers left.
Because there are no more restrictions for phone numbers that don’t work (first digit can’t be one or zero was the only restriction), the question then becomes : How many 6 digit numbers are possible (000000) can count , well we know that the biggest 6 digit number is 999999 and the smallest is 000000. That means there are 999999–000000+1 numbers between them inclusive. For those of you that are curious how I got the plus one, when you are counting the amount of numbers between let’s say a and b inclusive, the amount of numbers between them inclusive is |a-b| +1. Example : The amount of numbers between 2 and 13 inclusive is just |2–13|+1 which is 12. 2,3,4,5,6,7,8,9,10,11,12,13 is 12 numbers so |a-b|+1 works for the amount of numbers between a and b inclusive.
Anyways, back to the problem. 999999–000000+1 means there are 1000000 or 1 million possible 6 digit numbers. But that’s not the answer to the problem because each 1 of those 1 million 6 digit numbers needs a 7th digit which and be any number from 2–8 . This means that you need to multiply 1000000 by 8 to get 8 million possible phone numbers. If your wondering why I multiplied by 8, let’s say the number abcdef is one of the possible 6 digit numbers. If you add a 7th digit 2–9 to our number abcdef, then our number abcdef can be 2abcdef, 3abcdef, 4abcdef, 5abcdef, 6abcdef, 7abcdef, 8abcdef, 9abcdef.
Just a quick side note for any misconceptions, when I say the number abcdef, I don’t mean a times b times c times d times e times f, I mean a is the number in the hundred thousands place, b is the number in the 10 thousands place, c is the number in the thousands place, d is the number in the hundreds place, e is the number in the tens place, f is the number in the ones place.
Back to the problem, because there are 8 possible numbers for the 7th digit (AKA the first number in the phone number) you need to multiply the 1000000 different 6 numbers by 8 because each of those numbers has 8 variations.
In summary, there are 8*1000000 or 8 million different phone numbers whose digits aren’t 0 or 1
