Respuesta :
There are 10⁷ possible phone numbers from the digit 0 to 9.
What is Permutations?
Permutations are different ways of arranging objects in a definite order. It can also be expressed as the rearrangement of items in a linear order of an already ordered set.
Here, there are total 10 possible digits (0 to 9) we can use to create 7 digit phone numbers.
For first place there are 10 possible digits.
similarly for second place again 10 possibilities and so on.
So total number of phone number = 10 X 10 X 10 X 10 X 10 X 10 X 10
= 10⁷
Thus, there are 10⁷ possible phone numbers from the digit 0 to 9.
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Possible phone numbers can be 10 x 9 x 8 x 7 x 6 x 5 x 4 (without repetition) = 10!/3!.
10 10 10 - 10 10 10 10= [tex]10^{7} =1,00,00,000[/tex]. (with repetition)
What is number system?
A numeral system is a writing system for expressing numbers; that is, a mathematical notation for representing numbers of a given set, using digits or other symbols in a consistent manner.
There are 7 digit phone number represented with a XXX-XXXX .
So the first x can be 10 different numbers
let us take
10 ___ ___ ____ ____ ____ ____, but which ever number you use, it is then used up.
So then you only have 9 numbers left
10 x 9 x ___ x ___ x ___ x ___ x ___ .
Then, once that number is used it can't be used again, so on
10 x 9 x 8 x 7 x 6 x 5 x 4 (without repetition) = 10!/3!
If the repetition takes place then,
the first place have possibilities of 10 digits
10 __ __ - __ __ ___ __
Now, again repetition is allowed again there are possibilities of 10 digits.
10 10 __- __ __ __ __
and carrying the same way,
10 10 10 - 10 10 10 10= [tex]10^{7} =1,00,00,000[/tex].
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