Math challenges_xiang

[xiangliu2011]

Hi, does anyone work on the official guide to the GRE 2nd edition? I met some math problems on page 297, not sure how to figure out these problems.

Martha invited 4 friends to go with her to the movies. There are 120 different ways in which they can sit together in a row of 5 seats, one person per seat. In how many of those ways is Martha sitting in the middle seat?

From a box of 10 lightbulbs, you are to remove 4. How many different sets of 4 lightbulbs could u remove?

anyone could help?

[tommywallach]

Hey Xiang,

Every question has an explanation in the back. Are you confused in some ways about those explanations?

Also, in the future, please separate all individual questions into separate threads.

1. In this question, it's immaterial WHICH seat Martha is sitting in (i.e. it would be the same if she was in the first seat or the second seat or the third, for obvious reasons). So all we have to do is divide 120 by 5. There are 24 ways in which she's in each seat.

2. In this question, we actually have to use the combinatorics slots method.

_ _ _ _

4 slots. There are:

10 9 8 7

choices for each slot

HOWEVER, order doesn't matter, so we divide by the number of slots factorial to remove the duplicates:

(10 * 9 * 8 * 7) / (4 * 3 * 2 * 1) = 210

Hope that helps!

-t