Question

Dave wants to buy a new collar for each of his 4 dogs. The collars come in a choice of 6 different colors. 1. How many selections of collars for the 4 dogs are possible if repetitions of colors are allowed?2. How many selections of collars are possible if repetitions of colors are not allowed?

Answer 1

1296

360

Explanation:

Given that :

Number of dogs = 4

Different choices of collar available = 6

How many selections of collars for the 4 dogs are possible if repetitions of colors are allowed?

Then each of the 4 dogs can make 6 distinct choices :

6 * 6 * 6 * 6 = 6^4 = 1296

2. How many selections of collars are possible if repetitions of colors are not allowed?

If repetition isn't allowed :

Then we permutate :

6P4

Recall:

nPr = n! / (n - r)!

6P4 = 6! / (6 - 4)!

6P4 = 6! / 2!

6P4 = (6*5*4*3)

6P4 = 360