Hi, Fahim,
Quote:
Originally Posted by fahim mohammed
As to your answer to a 'teacher's' question as to the number of ways 2 objects can be arranged in a group of 3....being zero ( of course ' zero ' long predates either of us and has somehow managed to survive thus far )...I would say there is an ' x and y ' and a ' z '. The ' z ' being a joker.

We are all teachers. But I believe that question came from a joker.
In any case, it is said that, using the broader meaning of "permutation", with variables
n and
r, that is, "
n things taken
r at a time":
P(n,r) = 0 for r>n [The case for the recent question]
P(n,r) = n!/(nr)! otherwise
We must take 0! to be 1, which makes this work in the case of a true permutation (where r = n).
This value, P(
n,
r) is formally described as the number of
rpermutations of
n.
Best regards,
Doug