Six children — A, B, C, D, E, and F

gmat_guy666 wrote:Six children — A, B, C, D, E, and F — are going to sit in six chairs in a row. Child E must be somewhere to the left of child F. How many possible configurations are there for the children?

A)60
B)180
C)240
D)360
E)720

First, let's IGNORE the rule about child E seated somewhere to the left of child F.
When we ignore the rule, we can arrange the 6 children in 6! ways (= 720 ways)

Now recognize that, in HALF of those 720 arrangements, child E is seated somewhere to the LEFT of child F, and in the other HALF of those 720 arrangements, child E is seated somewhere to the RIGHT of child F.

So, the number of arrangements where child E is seated somewhere to the left of child F = (1/2)720 = 360

Answer: D

NOTE: This question is almost identical to this one: https://www.beatthegmat.com/counting-six ... tml#198825


Cheers,
Brent

Here are a few more to practice with:
- https://www.beatthegmat.com/permutation-t261691.html
- https://www.beatthegmat.com/vowels-and-c ... 49946.html
- https://www.beatthegmat.com/how-many-pos ... 77574.html

Cheers,
Brent

Hi gmat_guy666,

Brent's explanation is arguably the most efficient way to get to the correct answer. Here's a more drawn-out explanation for the correct answer:

We're given 6 spots:

_ _ _ _ _ _

And we have to put a child in each spot; E MUST be to the left of F though. Here's one possible way that this can occur:

E F _ _ _ _

In this option, any of the remaining 4 children can be placed in each of the 4 remaining spots, so we have….

E F (4)(3)(2)(1) = 24 options with E and F in the 1st and 2nd spots, respectively.

This pattern will occur over-and-over. For example….If E and F were in other places….

(4)E(3)(2)F(1) = 24 options with E and F in the 2nd and 5th spots, respectively.

So we really just need all of the possible placements for E and F, then we can multiply that result by 24…

While this is not necessarily the most efficient way to approach this task, the work isn't that hard….

E F _ _ _ _
E _ F _ _ _
E _ _ F _ _
E _ _ _ F _
E _ _ _ _ F

_ E F _ _ _
_ E _ F _ _
_ E _ _ F _
_ E _ _ _ F

_ _ E F _ _
_ _ E _ F _
_ _ E _ _ F

_ _ _ E F _
_ _ _ E _ F

_ _ _ _ E F

15 possible placements for E and F (given the restriction that E must be to the left of F).

15 x 24 = 360

Final Answer: D

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