factorial
fac
fÃĻk
fāk
to
ˈto:
to
rial
rÉĒəl
riēl
/fÃĻktˈɔːɹÉĒəl/

āχāĻ‚āϰ⧇āϜāĻŋāϤ⧇ "factorial"āĻāϰ āϏāĻ‚āĻœā§āĻžāĻž āĻ“ āĻ…āĻ°ā§āĻĨ

01

āĻĢā§āϝāĻžāĻ•ā§āϟāϰāĻŋāϝāĻŧāĻžāϞ, āĻĢā§āϝāĻžāĻ•ā§āϟāϰāĻŋāϝāĻŧāĻžāϞ

the product of all positive whole numbers from 1 to a given number
āωāĻĻāĻžāĻšāϰāĻŖ
In combinatorics, the factorial is used to determine the number of possible permutations of a set.
āϏāĻŽāĻžāĻŦ⧇āĻļ āϤāĻ¤ā§āĻ¤ā§āĻŦ⧇, āĻāĻ•āϟāĻŋ āϏ⧇āĻŸā§‡āϰ āϏāĻŽā§āĻ­āĻžāĻŦā§āϝ āĻŦāĻŋāĻ¨ā§āϝāĻžāϏ⧇āϰ āϏāĻ‚āĻ–ā§āϝāĻž āύāĻŋāĻ°ā§āϧāĻžāϰāĻŖ āĻ•āϰāϤ⧇ āĻĢā§āϝāĻžāĻ•ā§āĻŸā§‹āϰāĻŋāϝāĻŧāĻžāϞ āĻŦā§āϝāĻŦāĻšāĻžāϰ āĻ•āϰāĻž āĻšāϝāĻŧāĨ¤
01

āĻĢā§āϝāĻžāĻ•ā§āϟāϰāĻŋāϝāĻŧāĻžāϞ, āϗ⧁āĻŖāύ⧀āϝāĻŧāĻ•

multiplying a whole number by all the smaller whole numbers down to 1
āωāĻĻāĻžāĻšāϰāĻŖ
In probability theory, factorial calculations often appear in permutations and combinations.
āϏāĻŽā§āĻ­āĻžāĻŦā§āϝāϤāĻž āϤāĻ¤ā§āĻ¤ā§āĻŦ⧇, āĻĢā§āϝāĻžāĻ•ā§āϟāϰāĻŋāϝāĻŧāĻžāϞ āĻ—āĻŖāύāĻž āĻĒā§āϰāĻžāϝāĻŧāĻļāχ āĻŦāĻŋāĻ¨ā§āϝāĻžāϏ āĻāĻŦāĻ‚ āϏāĻ‚āĻŽāĻŋāĻļā§āϰāϪ⧇ āĻĻ⧇āĻ–āĻž āϝāĻžāϝāĻŧāĨ¤
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āύāĻŋāĻ•āϟāĻŦāĻ°ā§āϤ⧀ āĻļāĻŦā§āĻĻ
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āĻ…ā§āϝāĻžāĻĒ āĻĄāĻžāωāύāϞ⧋āĻĄ āĻ•āϰ⧁āύ