FACTDOUBLE
Returns the double factorial of a number.
Syntax:
FACTDOUBLE(number)
returns number!!, the double factorial of number, where number is an integer greater than or equal to zero.
For even numbers FACTDOUBLE(number) returns:
2*4*6*8* ... *number
For odd numbers FACTDOUBLE(number) returns:
1*3*5*7* ... *number
FACTDOUBLE(0) returns 1 by definition.
Example:
FACTDOUBLE(5)
returns 15.
FACTDOUBLE(6)
returns 48.
FACTDOUBLE(0)
returns 1.
Application:
Calculating the Number of Ways to Arrange Objects
Problem: You are a production manager at a toy company, and you need to arrange a set of uniquely shaped toy blocks on a display shelf. You have 6 different blocks, but you want to arrange them in a specific pattern. You want to arrange them in pairs, where the order of the pairs matters, but the order within each pair does not. The number of ways to arrange these 6 blocks in 3 pairs is given by (6−1)!!=5!!.
Using the FACTDOUBLE function, we can calculate this.
Formula: FACTDOUBLE(5)
Let's break down the calculation manually: 5!!=5×3×1=15
So there are 15 ways to arrange the 6 blocks in 3 pairs.
Here's how you would use the FACTDOUBLE function in a spreadsheet:
Number of Blocks | Calculation (Manual) | FACTDOUBLE Formula | Result | ||
|---|---|---|---|---|---|
A | B | C | D | ||
1 | 5 | 5!!=5×3×1 | FACTDOUBLE(5) | 15 | |
2 | 6 | 6!!=6×4×2 | FACTDOUBLE(6) | 48 | |
3 | 7 | 7!!=7×5×3×1 | FACTDOUBLE(7) | 105 | |
4 | 8 | 8!!=8×6×4×2 | FACTDOUBLE(8) | 384 | |
5 | 9 | 9!!=9×7×5×3×1 | FACTDOUBLE(9) | 945 |
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