Question 731105
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It's an nCr problem and not an nPr problem, because order does not matter.<br>
The total number of possible outcomes is choosing 2 of the 20 marbles: 20C2.<br>
The favorable outcomes are choosing 2 of the 12 red marbles AND 0 of the 8 blue marbles OR 2 of the blue marbles AND 0 of the 12 red marbles. Note that the "AND"s indicate multiplication and the "OR"s indicate addition:<br>
(12C2 * 8C0) + (8C2 * 12C0).<br>
{{{(C(12,2)*C(8,0)+C(8,2)*C(12,0))/C(20,2)}}}<br>
{{{(66*1+28*1)/190=94/190=47/95}}}<br>
Or you can get the answer without using nCr, by looking at the probabilities of picking one marble at a time, as the other tutor does.<br>