b. If n managers shake hands with each other exactlyonce, what is the total numb

Question

b. If n managers shake hands with each other exactlyonce, what is the total number of handshakes?

c. How many different ways can five managers be seated at around table? (Assume that if everyone moves to the right, theseating arrangement is the same)

d. How many different ways can n managers be seated ata round table?

I know the answer below but I need to know the steps so Ican learn how to do this, I give lifesaver rating, thanks

a. 10, b. n(n 1 )/2, c. 24, d.(n – 1 )!

a. 10, b. n(n 1 )/2, c. 24, d.(n – 1 )!

Explanation / Answer

This is a combinations/permutations problem. You should findon your calculator an operator that will do this for you. There isa formula for them but I don't know them well - look them up ongoogle. Combinations the order matters i.e. if 1 and 2 handshake thisis the same is 2 and 1. Permutations if 1 and 2 handshake this is different to 2 and1. a) The total number of people is 5, and each handshakeinvolves 2 people. Using a combination, 5C2 = 10. b) Same as before nC2. Plug this into the formula toget    n(n-1)/2 c) Unfortunately this problem you really need to draw it out.If you consider 1 person as being fixed, there are 4 ways of theothers being seated. If another is fixed, there is 3. If threeare fixed there is 2. So number of ways = 4*3*2 = 24 (or (5-1)!) d) Using the same logic as above, number of ways =(n-1)! Hope that helps

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