COMBIN

COMBIN(number, number_chosen)

Returns the number of combinations for a given number of items (without repetition).

number	The total number of "unique" items.
number_chosen	The number of items in each combination.

REMARKS

* This is also called the Binomial Coefficient.
* If any of the arguments are not numeric, then #VALUE! is returned.
* If "number" is not an integer, it is truncated.
* If "number" < 0, then #NUM! is returned.
* If "number_chosen" is not an integer, it is truncated.
* If "number_chosen" < 0, then #NUM! is returned.
* If "number" < "number_chosen", then #NUM! is returned.
* A combination is any set or subset of items, regardless of their internal order.
* Combinations are distinct from permutations, for which the internal order is significant.
* This is equivalent to FACT(n)/(FACT(k)*FACT(n-k)).
* You can use the COMBINA function to return the number of combinations (with repetition)
* You can use the FACT function to return the factorial of a positive whole number.
* You can use the MULTINOMIAL function to return the number of permutations for a given number of items (with duplicates).
* You can use the PERMUT function to return the number of permutations for a subset of objects or events (without repetition).
* You can use the PERMUTATIONA function to return the number of permutations for a subset of objects or events (with repetition).
* For the Microsoft documentation refer to support.microsoft.com

	A
1	=COMBIN(10, 6) = 210
2	=FACT(10)/(FACT(6)*FACT(4)) = 210
3	=FACT(10)/(FACT(3)*FACT(3)*FACT(2)) = 50400
4	=COMBIN(1,1) = 1 = a
5	=COMBIN(2,2) = 1 = ab
6	=COMBIN(3,2) = 3 = ab, bc, ac
7	=COMBIN(4,2) = 7 = ab, bc, cd, dc, ad, bd, ad
8	=COMBIN(5, 2) = 10
9	=COMBIN(6, 2) = 15
10	=COMBIN(7, 2) = 21
11	=COMBIN(8, 2) = 28
12	=COMBIN(10, 1)*COMBIN(10, 1)*COMBIN(10, 1) = 1000
13	=COMBIN("8", "4") = 70
14	=COMBIN(1, 2) = #NUM!
15	=COMBIN("text", 2) = #VALUE!
16	=COMBIN(2, "text") = #VALUE!

1 - How many different teams of 6 can you have from a group of 10.
2 - Same as Example 1 using the factorial function.
3 - How many different ways can the letters in the word STATISTICS be arranged. You cannot use the COMBIN function because all the items are not unique. S - appears 3 times, T appears 3 times, I appears 2 times.
4 - How many different 2 person teams can be made up from 8 people. answer 28 teams.
5 - How many combinations are there for a padlock with 3 numbers, answer 1,000 possibilities.