There is a four digit code. Repetition of the same code is not allowed. How many possible combinations can be possible?
I tried it as follows,
As repetition of the same code is not allowed so it should be $10P4$ choices?
Combination without repetition
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0@FahadUddin Which digits are allowed to be included? Can it be all digits (0 through 9), or is it only some of these digits? – 2013-05-22
4 Answers
If repetition of same is code is not allowed means "to repeating the same whole code again like 5555 can not come again in the series but 5554 can" as explained by the OP in his/her comment and again assuming that $0$ could be the first digit of these four digit codes,then the number of possible arrangements is $10^4$.
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0[Rule of product](http://en.wikipedia.org/wiki/Rule_of_product) – 2011-10-24
$10 P 4$ means no repetitions of the same digit, but you can repeat digits. You simply need to omit the cases where all the digits are the same, and there are exactly 10 such cases: 0000, 1111, and so forth up to 9999. So you have $10^4-10$ choices.
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1I agree that it's quite difficult to u$n$derstand the question... I think he means that a legal code is every sequence of 4 digits which is not simply a repetition of one digit, but I may be mistaken. – 2011-10-24
You have to apply formula for variations with repetition:
$\bar V_k^n=n^k\Rightarrow N=10^4$ , where N is number of choices.
If you mean that no digit can be repeated in any four digit code so that for example 9987 is not allowed because 9 appears twice then:
$P(n,k)=\frac{n!}{(n-k)!} =\frac{ 10!}{(10-4)!} = \frac{3628800}{720} = 5040$
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0This is an old question which has got few answers You are not contributing anything new. Besides, it would help if you learn and use $LaTeX$ – 2016-03-17