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  • Assuming that each number starts with 90 and that no digit appears more than once, how many 8-digit phone numbers can be created using only the digits 0 to 9?<

Assuming that each number starts with 90 and that no digit appears more than once, how many 8-digit phone numbers can be created using only the digits 0 to 9?

Option: 1

13560


Option: 2

20160


Option: 3

43020

 


Option: 4

32070


Answers (1)

best_answer

Let ABCDEFGHIJK be an 8-digit number.

Given that the first two digits of each number are 9 and 0.

As a result, the answer is 90CDEFGH.

Because repetition is not permitted and 9 and 0 are already taken, the digits available for place C are 1, 2, 3, 4, 5, 6, 7, 8, i.e. eight possible digits.

If one of them is taken at C, the number of digits available at D is now 7.

If one of them is taken at D, the number of digits available at E is now 6.

If one of them is taken at E, the number of digits available at F is now 5.

If one of them is taken at F, the number of digits available at G is now 4.

Similarly, at H, the possible digit is 3.

Thus,

8 \times 7 \times 6 \times 5 \times 4 \times 3=20160

Therefore, the total number of 6-digit numbers formed with given conditions is 20160.

 

Posted by

Rishi

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