Yesterday, Manhattan GMAT posted a GMAT question on our blog. Today, they have followed up with the answer:
Answer: E
Explanation:
Since we are asked for the number of combinations, this is a combinations question. As in all combinations questions, we start by diagramming the spots, then we fill in the blanks and multiply, and finally, divided by the factorial of the number of spots. In this particular question, there are two combinations questions in one, so we will do each one separately and then multiply.
For the paintings, there are 2 spots for 8 possible paintings:
Step 1: ___ x ___
Step 2: _8_ x _7_ = 56
Step 3: 56/2! = 28
For the sculptures, there are 3 spaces and 6 to choose from:
Step 1: ___ x ___ x ___
Step 2: _6_ x _5_ x _4_ = 120
Step 3: 120/3! = 120/6 = 20
Finally, we multiply these two together:
28 x 20 = 560