help rand
 <strong>rand</strong> Uniformly distributed pseudorandom numbers.
    R = <strong>rand</strong>(N) returns an N-by-N matrix containing pseudorandom values drawn
    from the standard uniform distribution on the open interval(0,1).  <strong>rand</strong>(M,N)
    or <strong>rand</strong>([M,N]) returns an M-by-N matrix.  <strong>rand</strong>(M,N,P,...) or
    <strong>rand</strong>([M,N,P,...]) returns an M-by-N-by-P-by-... array.  <strong>rand</strong> returns a
    scalar.  <strong>rand</strong>(SIZE(A)) returns an array the same size as A.
 
    Note: The size inputs M, N, P, ... should be nonnegative integers.
    Negative integers are treated as 0.
 
    R = <strong>rand</strong>(..., CLASSNAME) returns an array of uniform values of the 
    specified class. CLASSNAME can be 'double' or 'single'.
 
    R = <strong>rand</strong>(..., 'like', Y) returns an array of uniform values of the 
    same class as Y.
 
    The sequence of numbers produced by <strong>rand</strong> is determined by the settings of
    the uniform random number generator that underlies <strong>rand</strong>, RANDI, and RANDN.
    Control that shared random number generator using RNG.
 
    Examples:
 
       Example 1: Generate values from the uniform distribution on the
       interval [a, b].
          r = a + (b-a).*rand(100,1);
 
       Example 2: Use the RANDI function, instead of <strong>rand</strong>, to generate
       integer values from the uniform distribution on the set 1:100.
          r = randi(100,1,5);
 
       Example 3: Reset the random number generator used by <strong>rand</strong>, RANDI, and
       RANDN to its default startup settings, so that <strong>rand</strong> produces the same
       random numbers as if you restarted MATLAB.
          rng('default')
          rand(1,5)
 
       Example 4: Save the settings for the random number generator used by
       <strong>rand</strong>, RANDI, and RANDN, generate 5 values from <strong>rand</strong>, restore the
       settings, and repeat those values.
          s = rng
          u1 = rand(1,5)
          rng(s);
          u2 = rand(1,5) % contains exactly the same values as u1
 
       Example 5: Reinitialize the random number generator used by <strong>rand</strong>,
       RANDI, and RANDN with a seed based on the current time.  <strong>rand</strong> will
       return different values each time you do this.  NOTE: It is usually
       not necessary to do this more than once per MATLAB session.
          rng('shuffle');
          rand(1,5)
 
    See <a href="matlab:helpview([docroot '\techdoc\math\math.map'],'update_random_number_generator')">Updating Your Random Number Generator Syntax</a> to use RNG to replace
    <strong>rand</strong> with the 'seed', 'state', or 'twister' inputs.
 
    See also <a href="matlab:help randi">randi</a>, <a href="matlab:help randn">randn</a>, <a href="matlab:help rng">rng</a>, <a href="matlab:help RandStream">RandStream</a>, <a href="matlab:help RandStream/rand">RandStream/rand</a>,
             <a href="matlab:help sprand">sprand</a>, <a href="matlab:help sprandn">sprandn</a>, <a href="matlab:help randperm">randperm</a>.

    <a href="matlab:matlab.internal.language.introspective.displayOverloads('rand')">Other functions named rand</a>

    Reference page in Help browser
       <a href="matlab:doc rand">doc rand</a>

help factorial
 <strong>factorial</strong> Factorial function.
    <strong>factorial</strong>(N) for scalar N, is the product of all the integers from 1 to N,
    i.e. prod(1:N). When N is an N-D matrix, <strong>factorial</strong>(N) is the factorial for
    each element of N.  Since double precision numbers only have about
    15 digits, the answer is only accurate for N <= 21. For larger N,
    the answer will have the correct order of magnitude, and is accurate for 
    the first 15 digits.
 
    Class support for input N:
       float: double, single
       integer: uint8, int8, uint16, int16, uint32, int32, uint64, int64
 
    See also <a href="matlab:help prod">prod</a>.

    <a href="matlab:matlab.internal.language.introspective.displayOverloads('factorial')">Other functions named factorial</a>

    Reference page in Help browser
       <a href="matlab:doc factorial">doc factorial</a>

factorial(12)

ans =

   479001600

help nchoosek
 <strong>nchoosek</strong> Binomial coefficient or all combinations.
    <strong>nchoosek</strong>(N,K) where N and K are non-negative integers returns N!/K!(N-K)!.
    This is the number of combinations of N things taken K at a time.
    When a coefficient is large, a warning will be produced indicating
    possible inexact results. In such cases, the result is only accurate
    to 15 digits for double-precision inputs, or 8 digits for single-precision
    inputs.
 
    <strong>nchoosek</strong>(V,K) where V is a vector of length N, produces a matrix
    with N!/K!(N-K)! rows and K columns. Each row of the result has K of
    the elements in the vector V. This syntax is only practical for
    situations where N is less than about 15.
 
    Class support for inputs N,K:
       float: double, single
       integer: uint8, int8, uint16, int16, uint32, int32, uint64, int64
 
    Class support for inputs V:
       float: double, single
       integer: uint8, int8, uint16, int16, uint32, int32, uint64, int64
       logical, char
 
    See also <a href="matlab:help perms">perms</a>.

    <a href="matlab:matlab.internal.language.introspective.displayOverloads('nchoosek')">Other functions named nchoosek</a>

    Reference page in Help browser
       <a href="matlab:doc nchoosek">doc nchoosek</a>

help perms
 <strong>perms</strong>  All possible permutations.
    <strong>perms</strong>(1:N), or <strong>perms</strong>(V) where V is a vector of length N, creates a
    matrix with N! rows and N columns containing all possible
    permutations of the N elements.
 
    This function is only practical for situations where N is less
    than about 10 (for N=11, the output takes over 3 gigabytes).
 
    Class support for input V:
       float: double, single
       integer: uint8, int8, uint16, int16, uint32, int32, uint64, int64
       logical, char
 
    See also <a href="matlab:help nchoosek">nchoosek</a>, <a href="matlab:help randperm">randperm</a>, <a href="matlab:help permute">permute</a>.

    Reference page in Help browser
       <a href="matlab:doc perms">doc perms</a>

perms(1:3)

ans =

     3     2     1
     3     1     2
     2     3     1
     2     1     3
     1     2     3
     1     3     2

factorial(12)/(factorial(3)*factorial(2)*factorial(7))

ans =

        7920

diary off