4. Luke Skywalker is shopping for a new lightsaber because he lost his in an acc

Question

4. Luke Skywalker is shopping for a new lightsaber because he lost his in an accident. The lightsaber store has 6 blue, 5 green, and 3 red lightsabers in stock on their shelf. The lightsabers are all identical except for color. If Luke randomly picks a group of 4 lightsabers to try, what is the probability that this group has exactly 2 blue and 2 green lightsabers? If Luke randomly picks a group of 4 lightsabers to try, what is the probability that all 4 are the same color? All fourteen lightsabers are lined up randomly on a shelf at the store. What is the probability that the first and the last lightsaber are blue? How many different distinguishable ways can all fourteen lightsabers be arranged on the shelf? If all the lightsabers are lined up on the shelf, what is the probability that all the red ones are together? If all the lightsabers are lined up on the shelf, what is the probability that none of the blue ones are together? a) b) c) d) e) f)

Explanation / Answer

A) P(exactly 2 blue and 2 green ) = (6C2 * 5C2) / 14C4 = 150/1001 = 0.15

B) P(all are same color) = (6C4 + 5C4 )/14C4 = 20/1001 = 0.02

C) P(first and last are blue) = (12!/(5! * 3! * 4!) * 2!)/ (14!/(6! * 5! * 3!)) = 30/91 = 0.33

D) no of ways = 14! / (6! * 5! * 3!) = 168168

E) P(all the reds are together) = (12! * 3! / 6! * 5! * 3!) / (14! / 6! * 5! * 3!) = 0.033

F) P(none of the blue ones are together) = (9C6 * 6! * 8! / 3! * 5! * 6!) / (14! / 3! * 5! * 6!)

= 0.028

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