PERMUT function

[Guest]

I am curious as to why the PERMUT function returns the #NUM error value when
the number < number_chosen.

The function is PERMUT(number,number_chosen) where number is an integer that
describes the number of objects and number_chosen is an integer that
describes the number of objects in each permutation.

Why does Excel consider it an error to have a number < number_chosen? For
example, say I have 4 bits of data, each of which can be 2 numbers (a 0 or a
1). This results in number = 2 and number_chosen = 4, and the #NUM error.

I see there is a complex formula for calculating the total permutation, is
it mathematically undefined with a number < number_chosen? If not, I suggest
Excel allow a number < number chosen.

If it is mathematically undefined, I suggest a new function to calculate the
total number of possible permutations in cases when the number < number
chosen. The need to figure this out is common in programming fields, so I
think it would be frequently used.

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[Guest]

I think you have the wrong idea of what the PERMUT() function does. Take a
look in the help menu for an explanation of it.

And yes, it is mathematically impossible for number chosen to be greater
than the total number of elements you have.

For example, try selecting 60 cards from a standard deck of 52... it is
impossible because you don't have 60 cards to choose from!

 

[Harlan Grove]

Celeste wrote...

I am curious as to why the PERMUT function returns the #NUM error value when
the number < number_chosen. ....

From the rest of your post it's clear you don't understand what

permutations
are. An example: if you have a set of distinct items {a,b,c}, then all
of
them may be arranged as

a b c
a c b
b a c
b c a
c a b
c b a

So PERMUT(3,3) = 3! / 0! = 6. It's impossible to arrange 4 or more
items
drawn from this set of 3 items since there are *ONLY* 3 items available
to
arrange. Thus PERMUT(3,4) is an error.

That's the meaning of permutations in mathematics (combinatorics), and
that's the definition Excel uses. If you believe it means something
else,
then you have to change your understanding of what it means when using
Excel. Or try to find software that conforms to your understanding of
what permutations are (I doubt you'll have much success).

The function is PERMUT(number,number_chosen) where number is an integer that
describes the number of objects and number_chosen is an integer that
describes the number of objects in each permutation.

Wrong. PERMUT returns the number of permutations of items in subsets
of number_chosen items drawn without replacement from a set with number
items. The number of items in each permutation is always number_chosen.

Why does Excel consider it an error to have a number < number_chosen? For
example, say I have 4 bits of data, each of which can be 2 numbers (a 0 or a
1). This results in number = 2 and number_chosen = 4, and the #NUM error.

What you describe is 4 digit binary number, and there are 2^4 = 16 of
them. They're not considered permutations because the values of any of
the 4 digits are considered identical rather than distinct. Even if you
mean that the 4 items may be rearranged in different order, there would
still be only 2^4 = 16 distinct combinations.

If each of the items could attain 2 values distinct from the values
attained by any of the other items, then you still have only 16 sets
of sets of 4 items each, and there'd be PERMUT(4,4) = 24 permutations
of each of the 16 sets, so 16 * 24 = 384 distinct combinations. Or,
more generally, ni! * nv ^ ni, where ni is the number of items and nv
is the number of mutually distinct values each item may assume.

If it is mathematically undefined, I suggest a new function to calculate the
total number of possible permutations in cases when the number < number
chosen. The need to figure this out is common in programming fields, so I
think it would be frequently used.

Learn your terminology. A quick review of combinatorics (often taught
in finite/disctere math) would also be appropriate. No such function
is needed if you know a bit more math.