PlanMaker MULTINOMIAL: Count Arrangements of Repeated Types
Count repeated-category arrangements in PlanMaker, check factorial identities and understand its positive-count domain and POLYNOMIAL alias.
Verification status: See the evidence and test scope described in this guide. How formula examples are checked
Quick answer: =MULTINOMIAL(2,2,1) returns 30. It counts the distinct arrangements of five positions containing two objects of one type, two of another and one of a third, when objects of the same type are indistinguishable.
Availability and version history
- Introduced: Documented by the PlanMaker 2010 manual; the first introduction release is unknown.
- Availability: Listed in the 2026/NX English reference. No final supported-version endpoint is established.
- Scope: The checked desktop manuals do not establish identical behavior in every older, mobile or NX subscription build.
- Checked: October 14, 2026, against the official MULTINOMIAL reference. Documentation and independent calculations; no native PlanMaker test.
Syntax and PlanMaker’s documented domain
=MULTINOMIAL(Number1 [, Number2, Number3 ...])
The 2026 reference shows one required argument followed by optional additional values. It explicitly requires every supplied value to be at least 1. Use positive whole-number category counts for the examples below.
Do not import a zero-category rule from another spreadsheet. If a category has no objects, omit that category from this positive-count model rather than assuming PlanMaker accepts zero. The short entry does not establish all fractional-input coercions, so do not infer a truncation rule from FACT or FACTDOUBLE.
For positive integer counts a, b and c, the mathematical coefficient is:
(a+b+c)! / (a! * b! * c!)
The denominator removes reorderings among identical objects within each category. This is different from choosing one unordered subset, which is a use for COMBIN.
Reproducible category-count table
In a blank worksheet, set A1:E1 to Type A, Type B, Type C, Arrangements, and Factorial check. Enter A2:C5:
| Row | A | B | C | Expected D and E |
|---|---|---|---|---|
| 2 | 2 | 1 | 1 | 12 |
| 3 | 2 | 2 | 1 | 30 |
| 4 | 3 | 2 | 1 | 60 |
| 5 | 4 | 1 | 1 | 30 |
Enter =MULTINOMIAL(A2,B2,C2) in D2 and fill through D5. In E2 enter:
=FACT(A2+B2+C2)/(FACT(A2)*FACT(B2)*FACT(C2))
Fill E2 through E5. The FACT expression independently exposes the coefficient calculation for these small integer inputs. For row 3 it is 5!/(2!*2!*1!) = 120/4 = 30.
Keep A:C as counts, not labels. A formula with three explicit cell references also avoids assuming undocumented range-flattening behavior for a single range argument.
Reproduce the official example
In G2 enter:
=MULTINOMIAL(1,2,3,4,5)
The documented result is 37837800. In G3 enter =FACT(15)/(FACT(1)*FACT(2)*FACT(3)*FACT(4)*FACT(5)); the independent expected result is the same.
The total is 15 objects. The numerator is 1307674368000, the denominator is 34560, and their quotient is 37837800. This decomposition makes a missing or mistyped category count easier to detect than looking only at the final output.
Advanced example: build the same count in stages
For the row-3 counts 2, 2 and 1, choose the two positions for type A from five positions: COMBIN(5,2)=10. Then choose two of the remaining three positions for type B: COMBIN(3,2)=3. The remaining position belongs to type C.
Put =COMBIN(A3+B3+C3,A3)*COMBIN(B3+C3,B3) in F3. Its independent expected result is 30, matching D3. This staged model explains what the coefficient counts rather than treating it as a black box.
Changing the order of the categories does not change the total number of arrangements. In F4, =MULTINOMIAL(C3,A3,B3) also has an expected result of 30. The formula uses row 3 deliberately; it is a reordered check of that case, not a comparison with the row-4 dataset.
These are arrangements of category labels. If two objects within one category become distinguishable, or if certain positions are forbidden, this model no longer describes the same problem.
MULTINOMIAL and POLYNOMIAL are documented aliases
SoftMaker’s current entries explicitly state that MULTINOMIAL and POLYNOMIAL are identical. Despite the latter name, it does not evaluate a polynomial at x. For the same positive counts, both names represent the coefficient calculation described here.
The historical syntax needs care. The 2010 manual, pages 547–548, prints two required arguments, whereas the 2026 entry prints one. The available evidence does not establish the release in which that printed minimum changed, or whether older engines accepted an additional undocumented form. The examples here use at least three arguments and do not require resolving that historical ambiguity.
Troubleshooting and limits
- A zero count was supplied: PlanMaker’s current entry says every supplied value must be at least 1. Restructure the positive-count model instead of assuming another product’s accepted domain.
- A decimal count was supplied: objects are counted in whole units here. The reference does not describe a complete fractional-input rule.
- A very large result differs: factorials grow rapidly. The explicit FACT check is educational, not a guaranteed numerically safer algorithm for large counts.
- An error appears: inspect counts, required arguments and numeric types. The short source does not map every invalid case to a specific error token.
These formulas use English function names and commas, following the PlanMaker formula-entry guidance. Preserve input counts and the stated counting assumptions when comparing results across programs.