Amanda goes to the toy store to buy 1 ball and 3 different board games

Question

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

A. 9 
B. 12 
C. 14
D. 15
E. 60

peachfuzz · Answer

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

EMPOWERgmatRichC · Answer

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:  E

GMAT assassins aren't born, they're made,
Rich

OptimusPrepJanielle · Answer

This is a simple question that tests your concepts about combinations.

We need to select 1 ball out of 3 available and 3 board games out of 6 available.
This can be done in 3C1*6C3 ways = 3* \frac{{6!}}{{3!*3!}}  = 3*20 = 60

Option E

sowragu · Answer

Pretty Straight.

Choose 1 ball from 3 - 3C1 = 3/1 = 3
Choose 3 board games from 6 - 6C3 = (6*5*4)/(1*2*3)= 20

Total number of ways the selection can happen is = 3 * 20 = 60

rhine29388 · Answer

3C1*6C3=3*20 = 60

Correct answer - E

very_nice · Answer

I do not get logic. The explaination in the Kaplan book doesn't tell clearly why you multiply 3*20 and why you use the combination formula.
can someone explain why you multiply 3*20 and why you use combination insteat of permutation?

JeffTargetTestPrep · Answer

Amanda can select a ball in 3C1 = 3 ways and she can selected a board game in 6C3 = 6!/  = (6 x 5 x 4)/3! = (6 x 5 x 4)/(3 x 2 x 1) = 20. So, the total number of ways is 3 x 20 = 60.

Answer: E

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Amanda goes to the toy store to buy 1 ball and 3 different board games

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