Question

Tony wants to buy a new collar for each of his 4 dogs. The collars come in a choice of 9 different colors.

Answer 1

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 2

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 :$_nC_r=\frac{n!}{r!*(n-r)!}$

So no. of selections  of collars for 4 dogs are possible if repetitions of colors are not allowed

⇒$_9C_1 * _8C_1*_7C_1*_6C_1$

⇒$\frac{9!}{1!(9-1)!}*\frac{8!}{1!(8-1)!}*\frac{7!}{1!(7-1)!}*\frac{6!}{1!(6-1)!}$

⇒$\frac{9!}{1!(8)!}*\frac{8!}{1!(7)!}*\frac{7!}{1!(6)!}*\frac{6!}{1!(5)!}$

⇒$9*8*7*6$

⇒$3024$

Hence , 3024 no. of slections are possible if repetitions are not allowed.