Question

gia would like to place three tattoos on her body. she would like to have a tattoo on her right forearm, one right above her knee, and one on her back right below her neck. she walks into a tattoo parlor and asks the tattoo artist to show her any tattoo patterns that have angel, cupid, or skull in them. the tattoo artist shows her a collection of 26 such patterns. in how many different ways can gia tattoo her body with three of these patterns, given that the position of the tattoo on her body matters?

Explanation:

Step1: Identify the problem type

This is a permutation problem because the order (position) of the tattoos matters. The formula for permutations is \( P(n, r)=\frac{n!}{(n - r)!} \), where \( n \) is the total number of items, and \( r \) is the number of items to be selected and arranged.

Step2: Determine values of n and r

Here, \( n = 26 \) (total number of tattoo patterns) and \( r = 3 \) (number of tattoos to be placed in different positions).

Step3: Calculate the permutation

Substitute \( n = 26 \) and \( r = 3 \) into the permutation formula:

$$
LATEXBLOCK0
$$

Answer:

15600