Factorial Notation
For any natural number from 1 to n that is n factorial or n! Is expressed as,
1×2×3×....×(n-2)×(n-1)×n.
Note: the factorial notation that that can also be defined as a product of natural numbers from n to 1.
i.e, n!=n×(n-1)×(n-2)×...×3×2×1
5!=5×4×3×2×1=120
*Properties of factorial notation:-
1) 0! = 1
2) (m×n)! ≠ m!×n!
3) (m+n)! ≠ m!+n!
4) (m-n)! ≠ m!-n!
5) (m÷n)! ≠ m!÷n!
Ex 1) Find the value of 6!
Answer-
6 x 5 x 4 x 3 x 2 x 1= 720
Ex 2) Find n if (n+6)!=56(n+4)!
Solution-
 |
| Find n if (n+6)!=56(n+4)! |
Also read :- Permutation Combination
Ex Show that `\frac{\text {1}2!}{\text{5}!7!}+\frac{\text{1}2!}{\text{6}!6!}=\frac{\text{1}3!}{\text{6}!7!}`
Solution:
L.H.S. =
`\frac{\text{1}2!}{\text{5}!7!}+\frac{\text{1}2!}{\text{6}!6!}`
=`12!\left[\frac{\text{1}}{\text{5}!76!}+\frac{\text{1}}{\text{5}!66!}\right]`
(since, 7!=7×6! 6!=6×5!)
=`\frac{\text{12!}}{\text{5!}6!}\left[\frac{\text{13}}{\text{6 7}}\right]`
=`\frac{\text{12! 13}}{\text{(5! 6)*(6! 7)}}`
=`\frac{\text{13!}}{\text{6! 7!}}`
=R.H.S
