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A math teacher has 4 students in their class. To keep students engaged during class, they like to call on students to answer questions. During one particular class, they call on students 12 times, making sure to call on each student exactly 3 times. In how many different orders could the teacher have called on their students during this class?

I don't know if its 12! or something else

Aug 14, 2022

#1
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Here's my attempt:

Let the students be A, B, C, and D.

We basically have the question "How many ways can you arrange 3 A's, 3 B's, 3 C's, and 3 D's to form a 12 letter word?"

Note that the word will basically be the order you call on the students. So AAABBBCCCDDD means you call on A for the first 3 times, then B for the next 3 questions, then C, and finally D.

Can you take it from here?

Aug 14, 2022
#2
+275
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12!/3!*3!*3!*3!

would that be correct?

Aug 14, 2022
#3
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Yeah, that's what it would. Note that I'm not sure if my logic is correct.\(\)

BuilderBoi  Aug 14, 2022
edited by BuilderBoi  Aug 14, 2022