Yan was opening a new
restaurant, so she went to
the sign store to get
letters to make a sign to
hang above the
storefront. When she got
to the sign store, the only
letters they had in stock
were two copies of the
letter 'X,' two copies of
the letter 'E,' and one
copy of the letter 'V.' Yan
decided to buy all the
letters and use all of
them to make the name
of her store. How many
different names can she
give her store using these
5 letters? I got 120 but it's wrong. Sorry to post question from Brilliant. If you think, you can answer ...
answered by Steve earlier today
http://www.jiskha.com/display.cgi?id=1364826728
No problem! I'd be happy to help you with this question.
To find out how many different names Yan can give her store using the 5 letters ('X', 'X', 'E', 'E', 'V'), we can use the concept of permutations. In permutations, the order in which the letters appear matters.
Let's break down the question step by step:
1. First, we need to determine how many ways we can arrange all 5 letters. This is given by the formula for permutations of distinct objects, which is n!.
In this case, n = 5 (since we have 5 letters).
Therefore, the number of ways to arrange all 5 letters is 5! = 5 × 4 × 3 × 2 × 1 = 120.
However, there is one important detail we need to consider: the repeated letters. We have two copies of 'X' and two copies of 'E'.
2. To adjust for the repeated letters, we need to divide the total number of arrangements by the number of ways to arrange the repeated letters.
For the two 'X' letters, there are 2! = 2 permutations.
Similarly, for the two 'E' letters, there are also 2! = 2 permutations.
3. Finally, we divide the total number of arrangements by the arrangements of the repeated letters to get the final answer.
Number of arrangements = 5! / (2! × 2!) = 120 / (2 × 2) = 120 / 4 = 30.
Therefore, Yan can give her store 30 different names using the letters 'X', 'X', 'E', 'E', and 'V'.
So the correct answer is 30, not 120.
I hope this explanation helps! Let me know if you have any further questions or need clarification.