PERMUTATIONA function

PRO BASIC

The PERMUTATIONA function in Jspreadsheet Formulas Pro is a mathematical tool that calculates the total number of possible arrangements, or permutations, from a given set of items, and allows for repetition. This means an item can be selected more than once. For example, if you have a list of different colors and want to know how many combinations you can make with a certain number of choices, this function can give you that exact number. It's a handy function for statistical analysis and probability calculations.

Documentation

Returns the number of permutations for a given number of objects that can be selected from a set with repetition.

Syntax

PERMUTATIONA(number, number_chosen)

Parameter	Description
`number`	The total number of objects from which to choose.
`number_chosen`	The number of objects to arrange.

Behavior

The PERMUTATIONA function calculates the number of permutations for a given set of items with repetitions. This function takes two arguments:

number: The total number of items.
number_chosen: The number of items in each permutation.

Here is how it handles different types of inputs:

Empty Cells: If either of the arguments is an empty cell, the function will return a #VALUE! error.
Text: If either of the arguments is text instead of a number, the function will return a #VALUE! error.
Booleans: If either of the arguments is a boolean value (TRUE or FALSE), the function will treat TRUE as 1 and FALSE as 0.
Errors: If either of the arguments is an error, the function will return that error.
Negative Numbers: If either of the arguments is a negative number, the function will return a #NUM! error.
Non-integer Numbers: If either of the arguments is a non-integer number, the function will round it down to the nearest integer.

Common Errors

Error	Description
#VALUE!	This error occurs when either of the input arguments is non-numeric, an empty cell, or text.
#NUM!	his error occurs if either of the input arguments is negative.

Best practices

Always ensure that both input arguments are positive numbers. If you're unsure, you can use functions like ISNUMBER and IF to check the inputs and handle errors.

Be aware that the function rounds down non-integer numbers to the nearest integer. If you want to calculate permutations with fractional items, you'll need to adjust your inputs accordingly.

Remember that PERMUTATIONA allows for repetition of items in the set. If you want to calculate permutations without repetition, use the PERMUT function instead.

Be mindful of the computational limits of your spreadsheet software. Calculating permutations for large numbers can consume significant processing power and may cause your spreadsheet to become unresponsive.

Usage

A few examples using the PERMUTATIONA function.

PERMUTATIONA(5, 3) → Returns 125, the number of ways to arrange 3 objects chosen from 5 options when repetition is allowed.  
PERMUTATIONA(3, 4) → Returns 81, showing that 4 positions can be filled with 3 choices, allowing repeated selections.

Interactive Spreadsheet Demo

<html>
<script src="https://jspreadsheet.com/v11/jspreadsheet.js"></script>
<script src="https://jsuites.net/v5/jsuites.js"></script>
<link rel="stylesheet" href="https://jsuites.net/v5/jsuites.css" type="text/css" />
<link rel="stylesheet" href="https://jspreadsheet.com/v11/jspreadsheet.css" type="text/css" />

<link rel="stylesheet" href="https://fonts.googleapis.com/css?family=Material+Icons" />
<script src="https://cdn.jsdelivr.net/npm/@jspreadsheet/formula-pro/dist/index.min.js"></script>

<div id="spreadsheet"></div>

<script>
// Set your JSS license key (The following key only works for one day)
jspreadsheet.setLicense('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');

// Set the extensions
jspreadsheet.setExtensions({ formula });

// Create a new spreadsheet
jspreadsheet(document.getElementById('spreadsheet'), {
  worksheets: [{
    data: [
    [
        "Set Size",
        "Items Chosen",
        "Permutations with Repetition"
    ],
    [
        4,
        2,
        "=PERMUTATIONA(A2,B2)"
    ],
    [
        6,
        3,
        "=PERMUTATIONA(A3,B3)"
    ],
    [
        5,
        4,
        "=PERMUTATIONA(A4,B4)"
    ],
    [
        8,
        2,
        "=PERMUTATIONA(A5,B5)"
    ]
]
  }]
});
</script>
</html>

import React, { useRef } from "react";
import { Spreadsheet, Worksheet, jspreadsheet } from "@jspreadsheet/react";
import formula from "@jspreadsheet/formula-pro";
import "jsuites/dist/jsuites.css";
import "jspreadsheet/dist/jspreadsheet.css";

// Set license
jspreadsheet.setLicense('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');

// Set the extensions
jspreadsheet.setExtensions({ formula });

export default function App() {
    // Spreadsheet array of worksheets
    const spreadsheet = useRef();

    // Worksheet data
    const data = [
    [
        "Set Size",
        "Items Chosen",
        "Permutations with Repetition"
    ],
    [
        4,
        2,
        "=PERMUTATIONA(A2,B2)"
    ],
    [
        6,
        3,
        "=PERMUTATIONA(A3,B3)"
    ],
    [
        5,
        4,
        "=PERMUTATIONA(A4,B4)"
    ],
    [
        8,
        2,
        "=PERMUTATIONA(A5,B5)"
    ]
];

    // Render component
    return (
        <Spreadsheet ref={spreadsheet}>
            <Worksheet data={data} />
        </Spreadsheet>
    );
}

<template>
    <Spreadsheet ref="spreadsheet">
        <Worksheet :data="data" />
    </Spreadsheet>
</template>

<script>
import { Spreadsheet, Worksheet, jspreadsheet } from "@jspreadsheet/vue";
import "jsuites/dist/jsuites.css";
import "jspreadsheet/dist/jspreadsheet.css";
import formula from "@jspreadsheet/formula-pro";

// Set license
jspreadsheet.setLicense('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');

// Set the extensions
jspreadsheet.setExtensions({ formula });

export default {
    components: {
        Spreadsheet,
        Worksheet,
    },
    data() {
        // Worksheet data
        const data = [
    [
        "Set Size",
        "Items Chosen",
        "Permutations with Repetition"
    ],
    [
        4,
        2,
        "=PERMUTATIONA(A2,B2)"
    ],
    [
        6,
        3,
        "=PERMUTATIONA(A3,B3)"
    ],
    [
        5,
        4,
        "=PERMUTATIONA(A4,B4)"
    ],
    [
        8,
        2,
        "=PERMUTATIONA(A5,B5)"
    ]
]

        return {
            data
        };
    }
}
</script>

import { Component, ViewChild, ElementRef } from "@angular/core";
import jspreadsheet from "jspreadsheet";
import * as formula from "@jspreadsheet/formula-pro";

// Set your JSS license key (The following key only works for one day)
jspreadsheet.setLicense('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');

// Set the extensions
jspreadsheet.setExtensions({ formula });

@Component({
    standalone: true,
    selector: "app-root",
    template: `<div #spreadsheet></div>`
})
export class AppComponent {
    @ViewChild("spreadsheet") spreadsheet: ElementRef;
    // Worksheets
    worksheets: jspreadsheet.worksheetInstance[];

    // Create a new data grid
    ngAfterViewInit() {
        // Create spreadsheet
        this.worksheets = jspreadsheet(this.spreadsheet.nativeElement, {
            worksheets: [{
                data: [
    [
        "Set Size",
        "Items Chosen",
        "Permutations with Repetition"
    ],
    [
        4,
        2,
        "=PERMUTATIONA(A2,B2)"
    ],
    [
        6,
        3,
        "=PERMUTATIONA(A3,B3)"
    ],
    [
        5,
        4,
        "=PERMUTATIONA(A4,B4)"
    ],
    [
        8,
        2,
        "=PERMUTATIONA(A5,B5)"
    ]
]
            }]
        });
    }
}

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