Note that Rahul is using:
Probability = #desirable/#total
in which the denominator is "all the ways we can 'pull out' three coins from ten", and in which the numerator is "all the ways we can pull out 2 silver coins from 7 AND 1 gold coin from 3".
The question could also have been worded "If 3 coins are selected randomly one after another without replacement..." (If you're not replacing them, it doesn't matter whether you pull the three coins out simultaneously or one after another).
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We could have also solved by considering order. We want 2 silver and 1 gold, so:
(3/10)*(7/9)*(6/8) = 7/40
(G).........(S).....(S)
Because there are three arrangements in which we can have 2 silver and 1 gold (SSG, GSS, SGS), we have:
3*(7/40) = 21/40
Kaplan Teacher in Toronto
