In a certain school there are only Electrical Engineering students, civil Engine

Question

In a certain school there are only Electrical Engineering students, civil Engineering Students and Mechanical Engineering students. These students must take a class where they give a presentation. Students feel that the order of presentations is very important. If there are 9 students in the class and all give their presentation on one day how many different ways can you arrange the order of the presentations? If there are 18 students in the class but only 9 can give their presentation on Day 1, how many different orders of presentation can you have for Day 1. If the class contains 7 Mechanicals, 6 Civils and 5 Electricals and we require that the 9 individuals who give their presentations on Day 1 must include 3 Mechanicals, 3 Civils and 3 Electricals, how many different orders of presentation are there for Day 1? Suppose that all of the presentations that you counted in c part are equally likely. Suppose that you are one of the 5 Electrical Students. What is the probability that you will be the first one to give a presentation on Day 1?

Explanation / Answer

(a)

Here we need use permutation. Number of possible orders of presentation is 9! = 362880

(b)

Here we need to find out the possible orders of 9 presentation out of 18. So requried number of presentation is

18! / (18-9)!= 17,643,225,600

(c)

Number of ways of selecting 3 Mechanicals, 3 Civils and 3 electricals is C(7,3)C(6,3)C(5,3) = 7000

And number of ways of arranging 9 presentation is 9!.

So requried number of orders is 7000 * 9!

(d)

Number of ways of selecting students including you is C(7,3)C(6,3)C(5,2) = 7000

And number of orders in which you are first is 8!

So number of orders in which your presenation is first is 7000 * 8!

So requried probability is

(7000 * 8! ) / (7000 * 9!) = 0.1111

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