Number of ways of arranging seven digits into telephone numbers is example of a permutation or a combination?

i would think that it would be more of: there are ten digits you can choose from (0-9) and there are seven spaces so 10*10*10*10*10*10*10 = 10^7

Hi Jonathan Bloom This is an example of permutation as it involves arrangement of digits in 7 places. Order does matter since 1234567 is a different number from 7654321, hence permutation The solution: You can place any of the digits from 1 to 9 in the first place (0 is eliminated as placing it on the first digit would make it a 6 digit number) AND you can place any of the 10 digits in the 2nd place AND any of the 10 digits in the 3rd place and so on Thus 9*10*10*10*10*10*10 = 9000000 permutations are possible Shy

a) a permutation since it is order independent. However since you can have 555 as you pointed out it is really a variation on a permutation. What it is is identical to this problem. You have ten balls in a bowl. Each one is labeled as 0, 1, 2......9 with no duplicates. This is choice with replacement). So you can choose any one of the balls for every one for the ten phone number places. You can do this in ((10)^(10)) different ways. A permutation could be chosen in 10! ways if you picked without replacement. One thing is sure - It is not a combination!! Of course order matters, for years there was a bar (thankfully closed for 15 years) whose phone number was (703) 790-1314. They were open until 4:00 AM. At the time mine was (703) 790-1413 until I requested a change. I can't tell you how many drunks called me when I had been asleep. Fortunately the phone company granted me my request. It's kind of funny now, but it wasn't then.. .

Permutations is the answer. Remember this sentence: A combination lock is actually a permutation lock Phone numbers are similar to the number keys of so called combination locks.