2/15
There are 8C2 = 28 ways to choose 2 dimes from the 8 dimes in Annie's purse. There are 21C2 = 210 ways to choose 2 coins from the 21 coins in Annie's purse.
Of the 210 ways to choose 2 coins, 28 of the choices will result in 2 dimes being chosen. The probability of choosing 2 dimes is 28/210 = 2/15.
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Comment on nCk
The number of ways to choose k objects from n, when order does not matter, is ...
... n!/(k!(n -k)!)
For the computations above, we have ...
... 8C2 = 8·7/(2·1) = 28
... 21C2 = 21·20/(2·1) = 210
