# In how many ways can 2 motors and 2 switches be selected?

I'm not sure if order matters in this question. I believe that order matters the way that it is worded with selected, but any insight would help with the question below:

The supply department has 8 different electric motors and 5 different starting switches. In how many ways can 2 motors and 2 switches be selected for an experiment concerning a tracking antenna?

My answer: If order matters and repetition isn't allowed, I believe that it would be:

P(13,4) or 13 Pick 4


Note: This question is a suggested problem, not anything I need to hand in or school related.

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There are $\dbinom{8}{2}$ ways to choose the $2$ motors from the $8$ available.

For each such choice, there are $\dbinom{5}{2}$ ways to choose the switches, for a total of $$\binom{8}{2}\binom{5}{2}.$$

Note: $\dbinom{n}{k}$ is the standard mathematical notation for the number called $n$ Pick $k$ in the OP.

The numerical answer to the problem is $280$.

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Almost had it! Thank you – Ben Sewards Jan 31 '13 at 0:17
Isn't the answer this? -> (8!/6!)(5!/3!), which is 1120 – Ben Sewards Jan 31 '13 at 0:25
The usual interpretation of select (say for the motors) is that the order of selection doesn't count, all that matters is which pair of motors you ended up putting in the truck to take away. – André Nicolas Jan 31 '13 at 0:28
That makes more sense. – Ben Sewards Jan 31 '13 at 0:30