## A seven digit telephone number is of the form ABC-DEFG. In one particular state, the digit ‘A’ can be any digit except 0 and 1. Th

Question

A seven digit telephone number is of the form ABC-DEFG. In one particular state, the digit ‘A’ can be any digit except 0 and 1. The digits B and C can be any digit from 2 – 9. The digits D, E, F, and G can be any digit 0 – 9 except they can’t all be the same (e.g. 0000, 1111, 2222, ….etc.). How many seven digit phone numbers are possible with these restrictions?

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2 weeks 2022-12-26T10:11:03+00:00 1 Answer 0 views 0

1. The phone numbers that are possible with these restrictions are
4,480,000 Option C

### How many seven-digit phone numbers are possible with these restrictions?

It is imperative that you check the number of options available for each digit. After that, you take each of those numbers of options and multiply them together.
Because the phone number has seven digits, you will need to multiply all seven of those numbers together.
First digit: between 3 and 9.
In terms of mathematics, the only whole numbers that can be found between the digits 3 and 9 are the numbers 4, 5, 6, 7, and 8. That gives a total of five options to choose from.
Numbers between 1 and 8 make up the second and third digits.
According to mathematical definitions, the only whole numbers that may be found between 1 and 8 are 2, 3, 4, 5, 6, and 7. That gives a total of six options to choose from.
Last four digits: no restrictions, so there are 10 choices for each digit.
5 * 6 * 6 * 10 * 10 * 10 * 10
The product of the 7 numbers above is:
5 * 6 * 6 * 10 * 10 * 10 * 10 = 1,800,000
Now we have an issue. There is no option that comes close to the figure 1,800,000, and the closest possibility is a little less.
The conclusion is that this is a badly stated issue, and the term “between” is not being utilized appropriately in a mathematical fashion.
Let’s presume that by “any between 3 and 9”, 3 and 9 are included. As an additional note, both 1 and 8 falls inside this range.
We may now alter the solution to the following.
Because the phone number has seven digits, you must do a multiplication using seven separate integers.
First digit: between 3 and 9.
Between 3 and 9 means here: 3, 4, 5, 6, 7, 8, 9. That means there are 7 choices.
Second and third digits: between 1 and 8.
Between 1 to 8 is meant here 1, 2, 3, 4, 5, 6, 7, 8. That results in a total of eight options.
The last four numbers are up for interpretation, thus each one may take one of ten possible forms.
7 * 8 * 8 * 10 * 10 * 10 * 10
In conclusion, The product of the 7 numbers above is:
7 * 8 * 8 * 10 * 10 * 10 * 10 = 4,480,000