Factorials - Simplify (10! - 9!) / 8!

Question:

Simplify (10! - 9!) / 8!


Solution:

(10! - 9!) / 8!

= [(10 x 9 x 8!) - (9 x 8!)] / 8!

= [8! (10 x 9) - (9)] / 8!

= [8! (90 - 9)] / 8!

= [8! (81)] / 8!

= [ ̶8̶!̶ (81)] / ̶8̶!̶

= 81


Answer:

(10! - 9!) / 8! = 81


Video Solution:



Simplify (10! - 9!) / 8! A solved example from Factorials in Permutations and Combinations