C(6,1) = choose the matching pair = 6 choices. C(10,1) = 1 shoe from the other 10. Now you cannot choose the mate of that one, so you have 8 other shoes to choose from.
6 * 10 * 8 = 480 choices of "4 shoes". But then we must divide by 2, because the last two shoes could be chosen in either order.
That gives 240 choices - same as your teacher's answer, <span>but via a different route. </span>
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