UPDATE 12/17:  Corrected the answer to problem 14a (see comments below).

The Answer Key appears at the end of the review sheet, which is posted on the “Exam Reviews” page.  Let me know if you find any errors, or have any questions.

Best of luck,
Prof. Reitz

### 5 responses to “Final Exam Review Answer Key is posted”

1. I have a question about problem 14a.

The problem asks us to find the amount of 4 element lists where the first two elements must be vowels.

The answer I got was $3\cdot 2\cdot 8 \cdot 7$.

My reasoning is that there are three vowels in the set. Two of these vowels must be in the first two positions of this list. In the last two positions can go any of the leftover 7 consonants or the vowel that was not placed in the front of the list. In total, this gives us 8 elements to order in the last two positions. The answer in the answer key suggests that there are only 7 elements to order in the last two positions, which would be true if only consonants could be placed in the last two positions.

Is my thinking wrong?

You are absolutely right – the correct answer is $3\cdot 2\cdot 8\cdot 7$, or 336. I’ve updated the Answer Key accordingly.