Internal telephone numbers in a university are composed of 5 digits. The first two digits can form any integer between (and including) 61 and 75, the third digit is an integer between 1 and 9 and the last two each take any integer value. Assume that it is disallowed to have a phone number with last three digits being 100, 101, or 102. In such case, the total number of possible internal telephone numbers that start with the digit 7 is.....

Question

anonymous · Answer

is it 4500 - 15 = 4485

amistre64 · Answer

75
61
---
14+1 = 15 ways

1 to 9 = 9 ways (if we can count 1 and 9)

1000 ways - 3 = 997 ways for the ending

15*9*997 is what it looks like to me

amistre64 · Answer

is 134,595 an option?

anonymous · Answer

the first digit starts with a 7 mate, so its 5 possible choices times by 9 possible choices times by 100 possible choices for the last 2 digits including "00", since i have to avoid 100,101,102, i got to take of 15 possibilities so its 4500-15 = 4485

amistre64 · Answer

yeah, start with a 7 ... to many numbers to sort thru lol

70 71 72 73 74 75 = 6 ways then

6.9.997 is what I would see then

amistre64 · Answer

the last 3 digits can be from 000 to 999 (1000), excluding the 3 ways mentioned = 997 ways

amistre64 · Answer

61 to 75 = 15 ways, exclude the 6s and we get 6 ways to start

amistre64 · Answer

53,838 an option?

anonymous · Answer

so its 5400 - 18 = 5382, its not multiple choice =\

amistre64 · Answer

wait, im still reading the question a little off.  try this:

amistre64 · Answer

composed of 5 digits. 

first two digits, starts with a 7:  7 __    6 ways

3rd digit between 1 and 9:  9 ways

last two digits each take any integer value.
Assume that it is disallowed to have a phone number with last three digits being 100, 101, or 102

amistre64 · Answer

100 to 999 is where I was off at,

amistre64 · Answer

000 to 099 is 100 excluded ways, + the 3 mentioned total 103 excluded ways

1000
  103
-----
  897 ways total then sound right?

amistre64 · Answer

im still including that 3rd digit ....

amistre64 · Answer

00 to 99 is the last 2 digit options (100); exclude 00,01,02 (-3)

100-3 = 97 ways

6.9.97 = 5238

anonymous · Answer

thanks 5382 right? was that a typo error?