Excel COMBIN & PERMUT — Combinations vs Permutations (Does Order Matter?)

TL;DR — Both count how many ways to pick k things from n. PERMUT counts them when order matters (gold/silver/bronze is different from bronze/silver/gold); COMBIN counts them when order doesn't (a lottery ticket is the same numbers in any order). COMBIN is always the smaller — it's PERMUT divided by k!. The one question that picks the function: does order matter? Get it wrong and Excel gives no error, just a count off by a factor of k!. Two cousins, PERMUTATIONA and COMBINA, handle the case where repeats are allowed.

=PERMUT(10, 3)        ' ordered: 10×9×8 -> 720
=COMBIN(10, 3)        ' unordered: 720 / 3! -> 120
=COMBIN(49, 6)        ' lottery odds: pick 6 of 49 -> 13,983,816
=PERMUTATIONA(10, 3)  ' order matters, repeats allowed: 10^3 -> 1000
=COMBINA(10, 3)       ' order doesn't, repeats allowed -> 220

Search "combinations in Excel" and you'll get the syntax — =COMBIN(number, number_chosen) — but syntax was never the hard part. The hard part is knowing which function you need, because COMBIN and PERMUT answer nearly identical questions and return wildly different numbers, and Excel will happily give you the wrong one without a whisper of complaint. This page leads with the one distinction that decides everything.

What you'll learn

The mental model: does order matter? — the single question that chooses
Why COMBIN is always smaller than PERMUT (by exactly k!)
The 2×2 grid: order × repetition → four functions
Real examples: lottery odds, a podium, a committee, a PIN
Why picking the wrong one gives no error — just a silently wrong count
The #NUM! you'll hit when k > n or an argument goes negative

The mental model: does order matter?

Both functions start from the same setup — you have n distinct things and you're choosing k of them. The only thing that separates a combination from a permutation is whether rearranging the same chosen items counts as a new outcome:

Order matters → permutation → PERMUT. Gold, silver, and bronze medals: if Ana gets gold and Ben gets silver, that's a different result from Ben-gold, Ana-silver. The sequence is part of the answer.
Order doesn't matter → combination → COMBIN. A lottery ticket or a committee: picking {3, 17, 42} is the same selection as {42, 3, 17}. Only the membership matters, not the sequence.

That's the whole decision. Every other detail — the syntax, the cousins, the errors — hangs off this one question. Ask it before you type the function name, and you'll never reach for the wrong one.

Why COMBIN is always smaller

Here's the relationship, made concrete:

=PERMUT(10, 3)   ' -> 720
=COMBIN(10, 3)   ' -> 120

Both pick 3 from 10. PERMUT gets 720; COMBIN gets 120 — exactly six times smaller. That six is 3! (3×2×1), the number of ways to reorder any 3 chosen items. PERMUT counts each group of 3 once for every ordering; COMBIN collapses all those orderings into a single selection. So:

COMBIN(n, k) = PERMUT(n, k) / k!

This is why a combination is never bigger than the matching permutation, and it's a handy sanity check: if your "number of combinations" came out larger than the permutation count, you've swapped the two functions. The math also ties straight back to factorials — PERMUT(n,k) is n!/(n−k)! and COMBIN(n,k) is n!/(k!·(n−k)!) — which is why the FACT guide is the foundation under both.

The 2×2 grid: order × repetition

"Does order matter?" is the main axis. A second question — can an item be chosen more than once? — splits each answer in two, giving Excel's four counting functions:

	No repetition	Repetition allowed
Order matters	`PERMUT(n,k)`	`PERMUTATIONA(n,k)`
Order doesn't	`COMBIN(n,k)`	`COMBINA(n,k)`

=PERMUT(10, 3)        ' order, no repeat -> 720
=PERMUTATIONA(10, 3)  ' order, repeats allowed -> 10^3 = 1000
=COMBIN(10, 3)        ' no order, no repeat -> 120
=COMBINA(10, 3)       ' no order, repeats allowed -> 220

The …A cousins are the "repetition allowed" column. A 3-digit PIN where digits can repeat is PERMUTATIONA(10, 3) — order matters and 7-7-7 is legal, so it's 10³ = 1000, not PERMUT's 720. Choosing 3 scoops of ice cream from 10 flavors where you can double up on a flavor, and the order in the bowl doesn't matter, is COMBINA(10, 3) = 220. Most everyday problems live in the top-left/bottom-left "no repetition" column — but when repeats are on the table, the …A versions are what you want.

Worked examples

The functions come alive on real questions:

=COMBIN(49, 6)   ' lottery: 6 numbers from 49, order irrelevant -> 13,983,816
=PERMUT(8, 3)    ' race: gold/silver/bronze from 8 runners -> 336
=COMBIN(10, 3)   ' committee: any 3 people from 10 -> 120
=PERMUTATIONA(26, 4) ' 4-letter code, letters may repeat -> 456,976

Lottery odds. Pick 6 numbers from 49; order never matters. =COMBIN(49,6) gives 13,983,816 — so your odds of matching all six are about 1 in 14 million.
A podium. Three medals among 8 runners; order is the whole point. =PERMUT(8,3) = 336.
A committee. Three members from ten; a committee is a set, not a ranking. =COMBIN(10,3) = 120.
A code with repeats. Four letters, each of 26 and repeats allowed: =PERMUTATIONA(26,4) = 456,976 (26⁴).

Notice how the podium (336) dwarfs nothing, but the lottery (~14M) is enormous — combinatorial counts grow fast, which is the same explosive-multiplication theme that runs through PRODUCT and FACT.

The silent error: picking the wrong function

Here's the danger that makes the "does order matter?" question worth drilling: if you choose PERMUT when you meant COMBIN, Excel returns a perfectly valid number that is simply wrong — too large by a factor of k!. There's no #VALUE!, no red flag; 720 looks just as legitimate as 120. A lottery-odds calculation that used PERMUT instead of COMBIN would overstate the number of possible tickets 720-fold and quietly wreck every probability downstream.

The defense isn't a formula trick — it's the discipline of asking the order question out loud before you pick the function, and sanity-checking the magnitude (a combination should come out smaller than the matching permutation). This is a judgment problem, not a syntax problem.

The errors you will see

When these functions do error, the cause is usually a bad argument, not a typo:

=COMBIN(5, 10)   ' choosing more than you have -> #NUM!
=PERMUT(-1, 2)   ' negative arguments -> #NUM!
=COMBIN(10, 3.9) ' non-integers truncate -> treated as COMBIN(10, 3) = 120
=COMBIN(10, "x") ' non-numeric -> #VALUE!

#NUM! means the arguments are out of range: number_chosen bigger than number (you can't choose 10 things from 5 without repetition), or a negative value. Non-integer arguments are truncated to whole numbers before the count runs, and non-numeric arguments give #VALUE!. If a real problem genuinely allows choosing more than n (because repeats are allowed), that's your signal to switch to COMBINA or PERMUTATIONA, which don't have the k ≤ n restriction.

How ExcelMaster helps

Combinations versus permutations is a classic place to be confidently wrong — the formula runs, the number looks fine, and it's off by k!. Ask ExcelMaster "how many ways can 3 people from a team of 10 form a committee?" and it recognizes that order doesn't matter, returns =COMBIN(10,3), and explains why it's COMBIN and not PERMUT. Ask "what are the odds of winning a 6-from-49 lottery?" and it wires up =COMBIN(49,6) and turns it into a 1 in 13,983,816 probability.

Frequently asked questions

What's the difference between COMBIN and PERMUT in Excel?

PERMUT counts arrangements where order matters (a podium, a PIN, a ranking); COMBIN counts selections where order doesn't matter (a lottery, a committee). For the same n and k, COMBIN is always smaller — exactly PERMUT divided by k!. Ask "does rearranging the chosen items make a new outcome?" — yes → PERMUT, no → COMBIN.

How do I calculate combinations in Excel?

Use =COMBIN(n, k), where n is the total number of items and k is how many you choose. =COMBIN(49, 6) returns 13,983,816 — the number of ways to pick 6 numbers from 49 when order doesn't matter. If items can be chosen more than once, use COMBINA instead.

What are COMBINA and PERMUTATIONA for?

They're the "repetition allowed" versions. PERMUTATIONA(n, k) counts ordered arrangements where an item can repeat (a PIN where digits can repeat is PERMUTATIONA(10,3) = 1000). COMBINA(n, k) counts unordered selections with repeats allowed (3 ice-cream scoops from 10 flavors, doubles allowed, is COMBINA(10,3) = 220).

Why does COMBIN return a #NUM! error?

Because an argument is out of range — usually number_chosen is larger than number (you can't choose 10 from 5 without repetition), or an argument is negative. If your problem legitimately allows choosing more items than you have (because repeats are permitted), switch to COMBINA or PERMUTATIONA.

Does COMBIN handle decimals?

Non-integer arguments are truncated to whole numbers before counting, so =COMBIN(10, 3.9) behaves like =COMBIN(10, 3) and returns 120. Feed these functions whole numbers to avoid confusion.

Tested in

Tested in: Excel 365 (Windows 11) — last verified 2026-07-26.