Question 529143
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It depends.  Does the order in which the selection is made make a difference?  That is to say is a three student group that is chosen in the order Bill, Tom, and Alice the same or different from one was chosen in the order Tom, Alice, and Bill?


Order matters:  Number of permutations of 7 things taken 1 at a time TIMES permutations of 7 things taken 2 at a time:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \left(\frac{7!}{(7-1)!}\right)\left(\frac{7!}{(7-2)!}\right)\ =\ \left(\frac{7!}{6!}\right)\left(\frac{7!}{5!}\right)\ =\ 7\ \times\ 7\ \times\ 6]


Order does not matter:  Number of combinations of 7 things taken 1 at a time TIMES the number of combinations of 7 things taken 2 at a time:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \left(\frac{7!}{1!(7-1)!}\right)\left(\frac{7!}{2!(7-2)!}\right)\ =\ \left(\frac{7!}{6!}\right)\left(\frac{7!}{2!5!}\right)\ =\ 7\ \times\ 7\ \times\ 3]


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