Respuesta :
There are 9 ways to choose the collar color of the first dog, 8 ways to choose the collar color of the second dog (9 choices - the color for the first dog), 7 ways to choose the collar color of the third dog (9 choices - the colors for the first 2), and 6 ways to choose the collar color of the fourth dog (9 choices - the colors of the first three). Total is 9 * 8 * 7 * 6 = 3024 ways.
Answer:
3024
Step-by-step explanation:
Given: Tony wants to buy a new collar for each of his 4 dogs.
The collars come in a choice of 9 different colors.
To find : How many selections of collars are possible if repetitions of colors are not allowed?
Solution:
First we select collar from 9 collars . So, after selecting one collar, we will select next one collar from the remaining 8 collars and so on..
So, we will use the formula :[tex]_nC_r=\frac{n!}{r!*(n-r)!}[/tex]
So no. of selections of collars for 4 dogs are possible if repetitions of colors are not allowed
⇒[tex]_9C_1 * _8C_1*_7C_1*_6C_1[/tex]
⇒[tex]\frac{9!}{1!(9-1)!}*\frac{8!}{1!(8-1)!}*\frac{7!}{1!(7-1)!}*\frac{6!}{1!(6-1)!}[/tex]
⇒[tex]\frac{9!}{1!(8)!}*\frac{8!}{1!(7)!}*\frac{7!}{1!(6)!}*\frac{6!}{1!(5)!}[/tex]
⇒[tex]9*8*7*6[/tex]
⇒[tex]3024[/tex]
Hence , 3024 no. of slections are possible if repetitions are not allowed.
