P&C Problem

[sukhman]

The organizers of a week-long fair have hired exactly five security guards to patrol the fairgrounds at night for the duration of the event. Exactly two guards are assigned to patrol the grounds every night, with no guard assigned consecutive nights. If the fair begins on a Monday, how many different pairs of guards will be available to patrol the fairgrounds on the following Saturday night?
(A) 9 (B) 7 (C) 5 (D) 3 (E) 2
Answer D

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Hi sukhman,

As wordy and complex as this question looks, it actually has a really simple solution.

We have 5 security guards and 2 will be assigned to each day of the week. You're NOT allowed to have the same guard on back-to-back days though, so if you have 2 guards on Monday, you MUST have 2 DIFFERENT guards on Tuesday. This piece of information provides the big "shortcut" to this question.

The question asks for the total number of pairs (so the combination formula is implied) that COULD be assigned to Saturday.

Look back 1 day: on Friday, 2 guards were assigned (it doesn't really matter which 2), so those 2 COULD NOT be working on Saturday. That leaves 3 possible guards for Saturday:

[spoiler]3c2 = 3 pairs = Answer D[/spoiler]

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

[theCodeToGMAT]

For First Day, Monday = 5C2

Subsequent Days = 3c2 (skip 2 guards who did the duty a day before) = 3

Answer [spoiler][D][/spoiler]

[varun289]

can i post a simple approach to answer this tricky question


its says no guard for 2 consecutive day

so every day we left with balance 3 guys , just before day ,,,hope it clears and we skip that C2 c 5 equations

varun

[vinay1983]

The pair of guards alternate between 4 and 3. So sixth day (Saturday) 3 can be made to work.