Respuesta :
Number of ways to select 3 books from 13 books for adoption is 286 .
Step-by-step explanation:
A Permutation is an ordered Combination. When the order does matter it is a Permutation. There are basically two types of permutation:
- Repetition is Allowed: such as the lock above. It could be "333".
- No Repetition: for example the first three people in a running race. You can't be first and second.
Formula is given by:
[tex]nC_r= \frac{n!}{r! (n-r)!}[/tex] , where n is the number of things to choose from, and we choose r of them, no repetitions, order matters. Here , n=13 , r=3.
⇒ [tex]13C_3 = \frac{13!}{3!(13-3)!}[/tex]
⇒ [tex]13C_3 = \frac{13!}{3!(10)!}[/tex]
⇒ [tex]13C_3 = \frac{13(12)(11)10!}{3(2)(1)(10)!}[/tex]
⇒ [tex]13C_3 = 13(2)(11)[/tex]
⇒ [tex]13 C_3 = 286[/tex]
∴ Number of ways to select 3 books from 13 books for adoption is 286 .
