Question 426266
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No.  You want the number of ways to select 7 things from 10 things.


*[tex \LARGE \left(n\cr k\right\)] is the number of combinations of *[tex \Large n] things taken *[tex \Large k] at a time and is calculated by *[tex \Large \frac{n!}{k!(n\,-\,k)!}]


So begin with the formula and plug in your numbers:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \frac{10!}{7!(10\,-\,7)!}]


First, realize that


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ 10!\ =\ 10\ \times\ 9\ \times\ 8\ \times\ 7!]


So the arithmetic simplifies to:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \frac{10\ \times\ 9\ \times\ 8}{3\ \times\ 2}\ =\ 5\ \times\ 3\ \times\ 8\ =\ 120]




John
*[tex \LARGE e^{i\pi} + 1 = 0]
My calculator said it, I believe it, that settles it
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