Luke Skywalker is shopping for a new lightsaber because he lost his in an accide

Question

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.

a) 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?

b) If Luke randomly picks a group of 4 lightsabers to try, what is the probability that all 4 are the same color?

c) 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?

d) How many different distinguishable ways can all fourteen lightsabers be arranged on the shelf?

e) If all the lightsabers are lined up on the shelf, what is the probability that all the red ones are together?

f) If all the lightsabers are lined up on the shelf, what is the probability that none of the blue ones are

together?

Explanation / Answer

a) The probability that this group has exactly 2 blue and 2 green lightsabers is 6C2 * 5C2 / 14C2 = 15*10 / 91 = 1.6484

b) The probability that all 4 are the same color is 6C4 / 14C4 + 5C4 / 14C4 = 15/91 + 5/91 = 0.2198

c) The probability that the first and the last lightsaber are blue is 6P2 * 12! / 14! = 0.1648

d) The number of ways different distinguishable ways can all fourteen lightsabers be arranged on the shelf is 3!(6!5!3!)
e) The probability that all the red ones are together 12! / 14! = 0.0055
f) The probability that none of the blue ones are together 1 - 9!/14! = 0.9999958

Related Questions

Navigate

• Browse (All)
• Browse L
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.