MULTINOMIAL in WPS Spreadsheet: Repeated-Label Arrangements and Group Counts

• Introduced: documented by 2019-06-19 in the official WPS lesson; original introduction is not established.
• Availability: WPS Office for Windows Personal; no numeric release is stated in the edition metadata.
• Scope: exact current supported builds remain unverified. The Windows lesson does not establish equivalent availability in other WPS clients.
• Checked: October 14, 2026 against function-specific documentation. Examples were independently calculated; no native WPS test was performed.

=MULTINOMIAL(number1,[number2],...)

The first argument is required. Square brackets mark optional additional arguments and are not typed. The dated Windows Personal lesson describes 1–255 values; that historical statement does not establish the maximum of every current WPS build.

This guide uses positive integer counts. The lesson’s formal notes reject values below zero, while its walkthrough says values must be greater than zero. Because those statements leave a zero-boundary conflict, native zero-input behavior is not certified here. Fractional-input conversion is also not established by the captured text.

Examples use English function names and comma separators. Outputs below are independently calculated expectations.

=MULTINOMIAL(2,3,1)
=FACT(2+3+1)/(FACT(2)*FACT(3)*FACT(1))

Both expected results are 60, from 720 divided by 2×6×1. Keep the parentheses around the entire denominator in the expanded expression. Dividing by 2 and then multiplying by 6 would perform a different calculation.

Changing the argument order to =MULTINOMIAL(3,1,2) still gives 60 in this positive-integer model: the sum and the product of factorials are unchanged.

Arrange six labels containing two A labels, three B labels and one C label. Labels with the same letter are indistinguishable:

=MULTINOMIAL(2,3,1)

Expected distinct arrangements: 60. There are 6!=720 orders if every label were separately identifiable. Swapping the two A labels or permuting the three B labels creates duplicates, removed by dividing by 2! and 3!.

A smaller example uses two A labels and one B label: =MULTINOMIAL(2,1) gives 3, corresponding to AAB, ABA and BAA. This enumeration makes the repeated-label assumption visible.

Eight distinct people must join three named groups with sizes 3, 3 and 2:

=MULTINOMIAL(3,3,2)

Expected result: 560. Choose three of eight for Group A, then three of the remaining five for Group B; Group C receives the remaining two:

=COMBIN(8,3)*COMBIN(5,3)

This independently gives 56×10=560. Although Groups A and B have equal sizes, their names distinguish them. If group identities were intentionally ignored, the counting problem would change; MULTINOMIAL does not infer that change for you.

Enter numeric 2, 1 and 2 in A2:A4:

=MULTINOMIAL(A2:A4)

Expected result: 30, matching 5!/(2!*1!*2!). The official walkthrough demonstrates supplying a cell range to the function. These controls deliberately keep every referenced entry a positive integer; they do not establish a rule for text, logical values, blanks or errors inside ranges.

Change the middle count to 2 and the expected result becomes 90, from 6!/(2!*2!*2!). Keep the original and changed datasets separate if comparing outputs.

=MULTINOMIAL(1,1,1,1)
=MULTINOMIAL(4)

Expected results are 24 and 1. Four categories containing one object each behave like four distinct objects. A single category containing four identical labels has only one visible order.

A related two-category control is =MULTINOMIAL(3,2), expected 10, equal to =COMBIN(5,2). These equivalences follow the positive-integer factorial model and do not justify treating MULTINOMIAL as an unrestricted replacement for another function.

The source lists #NUM! for a negative argument and #VALUE! for a nonnumeric argument. Zero, decimals, mixed referenced types and exact conversion precedence remain separate unverified native cases. The primary examples avoid them.

Counts grow quickly. Large factorial expansions may overflow before division even when an algebraic simplification exists. No current-build overflow threshold or exact-integer precision boundary is established here. Use modest independently checkable controls when validating a workbook, and consult FACT for the ordinary factorial operation.

• WPS Academy: MULTINOMIAL lesson, 2019-06-19 (Chinese; Windows Personal scope).
• Editorial testing standards.

The direct WPS product lesson supports the stated function scope. Worked outputs are independent expectations, not captured native results or proof of support across all current WPS clients.