COMBINA

COMBINA(number, number_chosen)

Returns the number of combinations for a given number of items (with 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 "number" < 0, then #NUM! is returned.
* If "number" < "number_chosen", then #NUM! is returned.
* If "number_chosen" < 0, then #NUM! is returned.
* If "number" is not an integer, it is truncated.
* If "number_chosen" is not an integer, it is truncated.
* You can use the COMBIN function to return the number of combinations (without 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).
* This function was added in Excel 2013.
* For the Microsoft documentation refer to support.microsoft.com

	A
1	=COMBINA(10, 6) = 5005
2	=FACT(15)/(FACT(9)*FACT(6)) = 5005
3	=COMBINA(1,1) = 1 = a
4	=COMBINA(2,2) = 3 = ab, aa, bb
5	=COMBINA(3,2) = 6 = ab, bc, ac, aa, bb, cc
6	=COMBINA(4,2) = 10 = ab, bc, cd, dc, ad, bd, ad, aa, bb, cc, dd
7	=COMBINA(5, 2) = 15
8	=COMBINA(6, 2) = 21
9	=COMBINA(7, 2) = 28
10	=COMBINA(8, 2) = 36
11	=COMBINA(10, 1)*COMBINA(10, 1)*COMBINA(10, 1) = 1000
12	=COMBINA("8", "4") = 330
13	=COMBINA(1, 2) = 1
14	=COMBINA("text", 2) = #VALUE!
15	=COMBINA(2, "text") = #VALUE!

1 - How many different 6 digit numbers can you have when you consider all the 10 different digits (0 - 9) with repetition.
2 - Same as Example 1 using the factorial function.