SOLUTION: Debby has seven coins in her coin purse: 1 quarter, 2 dimes, 3 nickels, and 1 penny. If Debby shakes out three coins at random, what is the probability that the amount she has ou

Question 266268: Debby has seven coins in her coin purse: 1 quarter, 2 dimes, 3 nickels, and 1
penny. If Debby shakes out three coins at random, what is the probability that the
amount she has out is less than 25 cents?
(A) 17/35 (B) 18/35 (C) 17/49 (D) 18/49 (E) none of these

Answer by Edwin McCravy(20056) (Show Source): You can put this solution on YOUR website!


Of the 7 coins there are 6 non-quarters. If she doesn't get
the quarter, then the only way she could fail to get less
than 25 cents would be to get 2 dimes and 1 nickel.  Since 
there are only 2 dimes, to fail she must get them both, and 
since there are 3 nickels she can get 2 dimes and 1 nickel 
exactly 3 ways. So the number of successful ways to get less 
than 25 cents is the number of ways to get any 3 of the the 
6 non-quarters minus the 3 ways to get 2 dimes and a nickel.
That is,

 (6C3 - 3) ways

The number of ways of getting any 3 of the coins is 7C3.

So the desired probability is 



The correct choice is (A)

Edwin

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