# How to calculate permutations?

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?

• 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? – awkward Dec 20 '13 at 18:42
• AB is different than BA, and so on. – Amygdala Dec 20 '13 at 18:45

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

• 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 – Amygdala Dec 20 '13 at 19:42
• You are welcome! – Satish Ramanathan Dec 20 '13 at 20:17