Question

jillian has three different bracelets (x, y, and z) to give to her friends as gifts in any order she prefers. if bracelet y is chosen first, in how many ways can jillian give out the bracelets? 4 1 2 3

Explanation:

Step1: Identify the problem type

This is a permutation problem with a fixed first element. We know that bracelet Y is chosen first, so we only need to find the number of permutations of the remaining two bracelets (X and Z).

Step2: Calculate permutations of remaining bracelets

The number of permutations of \( n \) distinct objects is given by \( n! \). Here, we have \( n = 2 \) remaining bracelets (X and Z). The formula for permutations of \( n \) objects is \( P(n,n)=\frac{n!}{(n - n)!}=n! \). For \( n = 2 \), \( 2! = 2\times1=2 \). So there are 2 ways to arrange the remaining two bracelets after Y is chosen first.

Answer:

2 (corresponding to the option with value 2)