SOLUTION: In a certain city in the Philippines,all seven digit telephone numbers begin with 350. 1. How many telephone numbers maybe assigned to that city if the last four digits should not

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Question 1143232: In a certain city in the Philippines,all seven digit telephone numbers begin with 350.
1. How many telephone numbers maybe assigned to that city if the last four digits should not begin or end in zero?
2.How many telephone numbers if there's no restriction?
3.How many telephone numbers if there's no repetition of digits?
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
first 3 digits are 3 5 0.

1. how many telephone numbers may be assigned to that city if the last 4 digits can't begin or end with 0?

total number of possibilities is 1 * 1 * 1 * 9 * 10 * 10 * 9 = 8,100.

the first 3 digits are fixed.
the fourth digit has 9 possibilities (1 to 9).
the fifth and sixth digits each have 10 possibilities (0 to 9).
the seventh digit has 9 possibilities (1 to 9).

2. how many telephone numbers may be assigned to that city if the last 4 digits have no restrictions?

total number of possibilities is 1 * 1 * 1 * 10 * 10 * 10 * 10 = 10,000.

the first 3 digits are fixed.
the last 4 digits each have 10 possibilities (0 to 9).

3. how many telephone numbers may be assigned to that city if there is no repetition of digits?

total number of possibilities is 1 * 1 * 1 * 7 * 6 * 5 * 4 = 840.

the first 3 digits are fixed.
the fourth digit has 7 possibilities (0 to 9 except any of the numbers chosen for the first 3 digits.
the fifth digit has 6 possibilities (0 to 9 except any of the numbers chosen for the first 4 digits.
the sixth digit has 5 possibilities (0 to 9 except any of the numbers chosen for the first 5 digits.
the seventh digit has 4 possibilities (0 to 9 except any of the numbers chosen for the first 6 digits.

that's what i think.
give it a shot and see if it works for you.