Factorials - Find x if x/10! = 1/8! + 1/9!

Question:

Find x if x/10! = 1/8! + 1/9!


Solution:

x/10! = 1/8! + 1/9!

∴ x/10! = (10 x 9) / [(10 x 9) x 8!] + 10 / 10 x 9!

∴ x/10! = (10 x 9) / 10! + 10 / 10!

∴ x/10! = (10 x 9) + 10 / 10!

∴ x/10! = (90 + 10) / 10!

∴ x/ ̶1̶0̶!̶ = (90 + 10) / ̶1̶0̶!̶

∴ x = (90 + 10)

∴ x = 100


Answer:

x = 100 if x/10! = 1/8! + 1/9!


Video Solution:



Find x if x/10! = 1/8! + 1/9! A solved example on Factorials in Permutations and Combinations