Syntax
COMBIN(n, k)
| Parameter | Description |
|---|---|
| n | Parameter of the COMBIN function. |
| k | Parameter of the COMBIN function. |
Examples
Lottery combinations
Formula
=COMBIN(49, 6)
Returns 13,983,816. There are nearly 14 million ways to pick 6 numbers from 49 — that's your odds in a 6/49 lottery.
Team selection
Formula
=COMBIN(12, 5)
Returns 792. From 12 candidates, there are 792 possible 5-person teams.
Handshakes in a room
Formula
=COMBIN(20, 2)
Returns 190. In a room of 20 people, 190 unique handshakes are possible (each pair shakes hands once).
Common Errors
#NUM!
k cannot exceed n, and both must be non-negative. =COMBIN(3, 5) returns #NUM! because you can't choose 5 from 3.
#VALUE!
Non-numeric arguments return #VALUE!.
Tips
Order doesn't matter
COMBIN is for when order doesn't matter (choosing a committee). If order matters (assigning roles), use PERMUT instead.
Symmetry property
COMBIN(n, k) = COMBIN(n, n-k). Choosing 3 from 10 equals choosing 7 from 10 — there are 120 either way.
Probability calculations
For probability: favorable outcomes / total outcomes. E.g., P(exactly 3 heads in 5 flips) = COMBIN(5,3) × 0.5^5 = 10/32.
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