This is one of those logical combinatorics without a reliable formula. Let's make sure we understand what's being asked.

The wording allows for anywhere from 1 to six green balls to be in the boxes, however all the green balls need to be in adjacent boxes (consecutively numbered boxes).

So, if there's only one green ball, there are six ways this can be achieved (boxes 1 only, box 2 only, etc.). When there are two green balls they must be in consecutive boxes (1-2, 2-3, 3-4, 4-5, 5-6) of which five ways are possible.

As another green ball is added, there is one fewer way of satisfying the condition. Finally, when all six boxes are filled with green balls, we've reached the final way.

Adding them all up, 6+5+4+3+2+1 = 21 ways

relic wrote:This is one of those logical combinatorics without a reliable formula. Let's make sure we understand what's being asked.

The wording allows for anywhere from 1 to six green balls to be in the boxes, however all the green balls need to be in adjacent boxes (consecutively numbered boxes).

So, if there's only one green ball, there are six ways this can be achieved (boxes 1 only, box 2 only, etc.). When there are two green balls they must be in consecutive boxes (1-2, 2-3, 3-4, 4-5, 5-6) of which five ways are possible.

As another green ball is added, there is one fewer way of satisfying the condition. Finally, when all six boxes are filled with green balls, we've reached the final way.

Adding them all up, 6+5+4+3+2+1 = 21 ways

Relic,

This is indeed very helpful. Thanks a lot! What study preps would you recommend to improve Quant score?

kanha81 wrote:What study preps would you recommend to improve Quant score?

It seems like you've got plenty of good materials, but be careful, only studying the toughest questions is not the right approach. Make sure your doing well on more moderate-difficulty questions. Remember you don't get the tough ones until you get past the medium level ones.

The Official Guide is great for realistic questions, as is gmatfocus.com.