From her Collection of 9 Different Hats Ellen Wants to Wear one Different Hat GMAT Problem Solving

Question: From her collection of 9 different hats, Ellen wants to wear one different hat to school each day during a four-day week. How many different sequences of hats could she wear?

1. 9
2. 54
3. 1068
4. 2126
5. 3024

“From her collection of 9 different hats, Ellen wants to wear one different hat to school each day during a four-day week. How many different sequences of hats could she wear?”- is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been taken from the book “GMAT Official Guide Quantitative Review”. To solve GMAT Problem Solving questions a student must have knowledge about a good amount of qualitative skills. The GMAT Quant topic in the problem-solving part requires calculative mathematical problems that should be solved with proper mathematical knowledge.

Solution and Explanation:

Approach Solution:

There is only 1 approach to solving this problem

The given scenario states that Ellen has a collection of 9 different hats and wants to wear each of them every day for four days a week. This implies that every day she wants to wear a hat that is different from the other.
So on the first day, Ellen chooses to wear one hat out of which one of them. Further, on the second day, Ellen wants to wear another hat out of the 8 hats because she already wore one of them on the first day. Similarly, on the third day, she would wear a hat out of the 7 hats. On the 4th day, she would be able to wear a hat which she would choose from the rest of the 6 hats.
Thus, in that aspect, she is able to wear four hats in four days. Accordingly, to find the sequence in which she can wear all of the 9 hats can be contemplated as follows:
9 Χ 8 Χ 7 Χ 6 = 3,024
Hence, Ellen would be able to wear the 9 hats in 3,024 different sequences of hats.

Answer: E

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