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27 Dec 2015, 08:48
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Amanda goes to the toy store to buy 1 ball and 3 different board games. If the toy store is stocked with 3 types of balls and 6 types of board games, how many different selections of the 4 items can Amanda make?
A. 9
B. 12
C. 14
D. 15
E. 60
A. 9
B. 12
C. 14
D. 15
E. 60
30 Dec 2015, 18:10
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Amanda goes to the toy store to buy 1 ball and 3 different board games. If the toy store is stocked with 3 types of balls and 6 types of board games, how many different selections of the 4 items can Amanda make?
3! / 1!2! * 6! / 3!3!
=3*20=60
E. 60
3! / 1!2! * 6! / 3!3!
=3*20=60
E. 60
02 Jan 2016, 19:23
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Hi All,
The answer choices to this question provide an interesting 'shortcut' that you can use to avoid some of the math involved.
We're told that Amanda is going to buy 3 different board games (from a total of 6 different possible games). Since the order of the games does NOT matter, we're dealing with a Combination Formula calculation:
Combinations = N!/K!(N-K)! where N is the total number of items and K is the size of the subgroup.
N = 6 and K = 3
6!/3!(6-3)! = (6)(5)(4)(3)(2)(1)/(3)(2)(1)(3)(2)(1) = (6)(5)(4)/(3)(2)(1) = 20 different combinations of 3 games.
Since we already have 20 different options, including a ball will only INCREASE the number of possibilities. There's only one answer that fits...
Final Answer:
GMAT assassins aren't born, they're made,
Rich
The answer choices to this question provide an interesting 'shortcut' that you can use to avoid some of the math involved.
We're told that Amanda is going to buy 3 different board games (from a total of 6 different possible games). Since the order of the games does NOT matter, we're dealing with a Combination Formula calculation:
Combinations = N!/K!(N-K)! where N is the total number of items and K is the size of the subgroup.
N = 6 and K = 3
6!/3!(6-3)! = (6)(5)(4)(3)(2)(1)/(3)(2)(1)(3)(2)(1) = (6)(5)(4)/(3)(2)(1) = 20 different combinations of 3 games.
Since we already have 20 different options, including a ball will only INCREASE the number of possibilities. There's only one answer that fits...
Final Answer:
GMAT assassins aren't born, they're made,
Rich
