SOLUTION: please help A teacher has a set of 12 problems to use on a math exam. THe teacher makes different versions of the exam by putting 10 questions on each exam. How many different e

Question 40623: please help
A teacher has a set of 12 problems to use on a math exam. THe teacher makes different versions of the exam by putting 10 questions on each exam. How many different exams can the teacher make?
please explain how to get the answer
a)12!/11!
b)66
c)132
Answer by longjonsilver(2297) (Show Source): You can put this solution on YOUR website!
Imagine the 10 placeholders for the questions:
_ _ _ _ _ _ _ _ _ _

First question: 12 possible questions can go there.
Second question: now 11 possible questions --> 12*11 ways of having these first 2 questions.
and so on, until we have 12*11*10*9*8*7*6*5*4*3. Work this out for the answer.

jon.
======================================
i have just re-read the question and i dont think i have answered what the question wanted.

I think the Q wanted sets of 10 questions... how many of those are there, which is a far smaller set. Whereas i gave you all the different orderings of 10 questions.

What we need is "a set of 10" and therefore also "a set of 2, not used".

Given 12 questions: ABCDEFGHIJKL we need to look at the "2 not used":

AB
AC
AD
AE
AF
AG
AH
AI
AJ
AK
AL

then
BC
BD
BE
etc

This tells us: 2 placeholders: _ _ and there are 12 in the first and then 11 in the second: So, 12*11 --> 132 variations.

So, there are therefore 132 different sets of 10 questions we can have.

Jon
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