The city needs a Supreme Court with five judges. There are 100 candidates. a. Co

Question

The city needs a Supreme Court with five judges. There are 100 candidates.

a. Consider the case where each judge has equal power. Al, Bob, Charlie, Dave, and Edward are five people in the pool of 100 candidates. What is the probability that they will be chosen to serve on the Supreme Court? Round responsibly.

b. Consider the whacky case where the judges don't have equal power: one is the "Grand Poobah", one is the "Vice-Grand Poobah", one has to take a ridiculous amount of notes during meetings (this one is called a secretary), one has to keep track of all the money they spend (the treasurer), and the last one is the court jester. Al, Bob, Charlie, Dave, and Edward are five people in the pool of 100 candidates. What is the probability that Al is chosen Grand-Poobah, Bob is chosen Vice-Grand-Poobah, Charlie is chosen secretary, Dave is chosen treasurer, and Edward is chosen courth jester... all to seve on this new, whacky City Supreme Court? Round Reasonably.

Explanation / Answer

Let's write given information

There are 100 candidates. that is n = 100

a. We are given that the case where each judge has equal power.

Al, Bob, Charlie, Dave, and Edward are five people in the pool of 100 candidates.

We want to find the probability that they will be chosen to serve on the Supreme Court.

Since the order is not important so we can use combination to find the total ways = 100C5 = "=COMBIN(100,5)" This is an excel command

So total ways = 75287520

Therefore required probability = 1/ 75287520 = 0.0000000132824 = 0.00000001 (after rounding eight decimal places.

part 2)

We want to find the probability that they will be chosen to serve on the Supreme Court in the specified order.

Since the order is now important so we can use permutation to find the total ways = 100P5 = "=PERMUT(100,5)" This is an excel command

So total ways = 9034502400

Then the required probability =1/ 9034502400 = 1.10687E-10 = 0.000000000110687 = 0.0000000 = 0 (rounded up to 8 decimal places and which is approximately zero.

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