1
$\begingroup$

I'm trying to figure out all possible permutations/combinations of an idea in my head.

Say I start with 60 objects. I can use anywhere between 1 and 24 of those objects to create a pattern. The objects can be arranged in any order in this pattern, but within the limitations of 1 being the minimum objects used and 24 being the maximum.

How many patterns could I make total and how would I calculate it?

$\endgroup$
  • $\begingroup$ Does the order of objects in the pattern matter? For example, is the pattern AB the same as the pattern BA, or are those two different patterns? $\endgroup$ – awkward Dec 20 '13 at 18:42
  • $\begingroup$ AB is different than BA, and so on. $\endgroup$ – Amygdala Dec 20 '13 at 18:45
1
$\begingroup$

If objects are distinguishable, then don't you think the answer will be the summation of ${60\choose1}\cdot1!+{60\choose2}\cdot2!+\dots+{60\choose24}\cdot24!$

Thanks

Satish

$\endgroup$
  • $\begingroup$ That worked perfectly. And in case anyone was interested, the sum is equal to: 4,818,692,886,000,000,000,000,000,000,000,000,000,000,000 Or, in text: four tredecillion, eight hundred eighteen duodecillion, six hundred ninety-two undecillion, eight hundred eighty-six decillion $\endgroup$ – Amygdala Dec 20 '13 at 19:42
  • $\begingroup$ You are welcome! $\endgroup$ – Satish Ramanathan Dec 20 '13 at 20:17

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.