Question 419253
1. A quiz consists of 5 multiple-choice questions, each has three possible answers. In how many different ways can the quiz be answered if an answer is chosen for each question?
I said 5 x 3 = 15
It's 3^5 = 243 possibilities.
If the answers for each are A, B & C, you can have
A A A A A
A A A A B
A A A A C
A A A B A
A A A B B
A A A B C
A A A C A
A A A C B
A A A C C
etc.
You can see there are more than 15.
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2. In how many ways can three different math books and four different English books be arranged in a row if the books for each subject are placed together?
3 x 4 = 12
With the math books first, the 1st book can be 1 of 3, the 2nd 1 of 2, then 1
= 3*2*1 = 6
For the English books, it's 4*3*2 *1 = 24
6*24 = 144
Then the English books can be first, --> 288 ways.
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3. In how many different ways can three finalists be selected from 15 job applicants for a second round interview?
15 x 3 = 45
It's 15*14*13 = 2730
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4. Fifteen dogs enter a Goofy Dog contest. In how many different ways can a champion, a first runner-up, and a second runner-up be selected?
15 x 3 = 45 
Same as #3, 2730