Advice 1: How to calculate the number of combinations

Suppose that the given N elements (numbers, objects, etc.). You want to know the number of ways those N elements can be arranged in a row. In more precise terms, you want to calculate the number of possible combinations of these elements.
How to calculate the number of combinations
Instruction
1
If it is assumed that the number includes all N elements, and none is repeated, it is the problem of the number of permutations. The solution can be found by simple reasoning. First in the row can be any of N elements thus obtained N options. In the second place, moreover, which was already used for the first place. Consequently, each of the N already found options there are (N - 1) second place, and the total number of combinations is N*(N - 1).
The same reasoning can be repeated for the remaining elements of the series. For the last place there remains only one option — the last remaining item. For last two options, and so on.
Therefore, for a number of N distinct items the number of possible permutations is equal to the product of all the integers from 1 to N. This work is called factorial N and is denoted N! (read "n factorial").
2
In the previous case, the number of possible elements and number of seats number of match and the number is equal to N. But it is possible that in a number of smaller places than there are possible elements. In other words, the number of elements in the sample is equal to some number M, where M < N. In this case the problem of determining the number of possible combinations can have two different options.
First, you may need to count the total number of possible ways to rank M elements of N. Such methods are referred to as placements.
Second, the researcher may be interested in a number of ways to choose M elements from N. the order of the elements is not important, but any two choices must differ by at least one element. Such methods are called combinations.
3
To find the number of permutations of M elements from N, one can resort to the same way of reasoning as in the case of permutations. In the first place is still can stand N elements, the second (N - 1), and so on. But for last place in the number of possible variants is equal to one and (N - M + 1), since, when the placement is finished, there remain (N - M) unused elements.
Thus, the number of allocations of M items from N is equal to the product of all the integers from (N - M + 1) to N, or, equivalently, the private N!/(N - M)!.
4
It is obvious that the number of combinations of M elements of N will be less than the number of placements. For each possible combinations is M! possible placements that depend on the order of the elements of the combination. Therefore, in order to find this amount, you need to divide the number of allocations of M items from N is N!. In other words, the number of combinations of M items from N is N!/(M!*(N - M)!).

Advice 2: How to calculate a factorial

The factorial of a natural number is the product of all previous natural numbers, including the number itself. The factorial of zero equal to one. It seems that to calculate the factorial of a number is very easy – just multiply all the natural numbers not exceeding a certain. However, the value of the factorial grows so quickly that some calculators don't cope with this task.
How to calculate a factorial
You will need
  • calculator, computer
Instruction
1
To calculate the factorial of a natural number, multiply all the natural numbers not exceeding this. Each number is counted only once. As a formula this can be written as follows:n! = 1*2*3*4*5*...*(n-2)*(n-1)*n, Gda is a natural number a factorial of which you want to calculate.
0! considered as equal to one (0!=1).With an increase of the argument the value of factorial increases very quickly, so the usual (financial) calculator for the factorial of 15 is it may give an error message.
2
To calculate the factorial of large positive numbers, take a calculator. That is, the calculator on the keyboard which are marked with math functions (cos, sin, √). Enter to calculator original number, and then click calculate the factorial. Usually, this button is denoted as "n!" or similar (instead of the letter "n" might stand for "N" or "x", but the exclamation mark "!" factorial symbol should be present in any case).
For large values of the argument calculation results are displayed in "exponential" (exponential) form. For example, the factorial of 50 is presented in the form: e 3,0414093201713378043612608166065+64 (or similar). To get the result of the calculation in the normal manner, attribute to the number displayed before the "e" as many zeros as indicated after the "e+" (of course, if enough space).
3
To calculate the factorial of a number in the computer, run the calculator (standard Windows calculator). To do this, locate its image on the desktop or click on the button "start" and "Run". Then, type in the appeared window "calc" and hit "OK". View: how did you start the program "Calculator". If the picture resembles the ordinary "accounting" calculator, switch it to "engineering" mode. To do this, simply click on the item "View" and select in the list of options the string "Engineering".
After this, repeat the same steps that are listed in the previous paragraph of the instruction - enter the number and press "n!".
4
"Calculate the factorial of a number is possible without the use of computer technology. To do this, simply print a table of factorials. Since the values of the factorial are increasing very rapidly, it is feasible to only print out factorials of numbers from 0 to 50. However, the practical application of such tables is very doubtful. Firstly, the entry of such multi-digit numbers will take a very long time, and secondly, the probability of entry errors, and, thirdly, it is not clear where to enter such a long number. Neither the display of the calculator or the Excel cell just barely fits so many figures.
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