QuestionDetails: Question: Hand shakes and Round tables a) Five managers gather

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QuestionDetails: Question: Hand shakes and Round tables a) Five managers gather for a meeting.If each managershakes hands with each other manager exactly once, what is thetotal number of handshakes? b)If n managers shake hands with each other exactly once, whatis the total number of handshakes? c) How many different ways can five managers be seated at a round table?(Assume that if everyone moves to the right, theseating arrangment is the same) d)How many different ways can n managers be seated at a roundtable? Please i need help with this question. step-step workingplease. QuestionDetails: Question: Hand shakes and Round tables a) Five managers gather for a meeting.If each managershakes hands with each other manager exactly once, what is thetotal number of handshakes? b)If n managers shake hands with each other exactly once, whatis the total number of handshakes? c) How many different ways can five managers be seated at a round table?(Assume that if everyone moves to the right, theseating arrangment is the same) d)How many different ways can n managers be seated at a roundtable? Please i need help with this question. step-step workingplease. QuestionDetails: Question: Hand shakes and Round tables a) Five managers gather for a meeting.If each managershakes hands with each other manager exactly once, what is thetotal number of handshakes? b)If n managers shake hands with each other exactly once, whatis the total number of handshakes? c) How many different ways can five managers be seated at a round table?(Assume that if everyone moves to the right, theseating arrangment is the same) d)How many different ways can n managers be seated at a roundtable? Please i need help with this question. step-step workingplease.

Explanation / Answer

a -> b b -> c c -> d d -> e (remember, a-> b is the same as b -> a and is counted only once) a -> c b -> d c -> e a -> d b -> e a -> e
This makes 10 handshakes.
B) The number of handshakes can be put into a simple equationwith n:
Number of handshakes = n(n-1)/2
C) 24 times: Five men, a, b, c, d, and e. In each offour positions, 1, 2, 3, 4, and 5.
a1 b2 c3 d4 e5 a1 b2 c4 d3 e5 a1 b3 c2 d4 e5 a1 b3 c4 d2 e5 a1 b2 c3 d4 e5 a1 b2 c4 d3 e5
a1 b2 c3 d5 e4 a1 b2 c5 d3 e4 a1 b3 c2 d5 e4 a1 b3 c5 d2 e4 a1 b2 c3 d5 e4 a1 b2 c5 d3 e4
a1 b2 c5 d4 e3 a1 b2 c4 d5 e3 a1 b5 c2 d4 e3 a1 b5 c4 d2 e3 a1 b2 c5 d4 e3 a1 b2 c4 d5 e3
a1 b5 c3 d4 e2 a1 b5 c4 d3 e2 a1 b3 c5 d4 e2 a1 b3 c4 d5 e2 a1 b5 c3 d4 e2 a1 b5 c4 d3 e2 a1 b2 c3 d5 e4 a1 b2 c5 d3 e4 a1 b3 c2 d5 e4 a1 b3 c5 d2 e4 a1 b2 c3 d5 e4 a1 b2 c5 d3 e4
a1 b2 c5 d4 e3 a1 b2 c4 d5 e3 a1 b5 c2 d4 e3 a1 b5 c4 d2 e3 a1 b2 c5 d4 e3 a1 b2 c4 d5 e3
a1 b5 c3 d4 e2 a1 b5 c4 d3 e2 a1 b3 c5 d4 e2 a1 b3 c4 d5 e2 a1 b5 c3 d4 e2 a1 b5 c4 d3 e2 a1 b2 c5 d4 e3 a1 b2 c4 d5 e3 a1 b5 c2 d4 e3 a1 b5 c4 d2 e3 a1 b2 c5 d4 e3 a1 b2 c4 d5 e3
a1 b5 c3 d4 e2 a1 b5 c4 d3 e2 a1 b3 c5 d4 e2 a1 b3 c4 d5 e2 a1 b5 c3 d4 e2 a1 b5 c4 d3 e2 a1 b5 c3 d4 e2 a1 b5 c4 d3 e2 a1 b3 c5 d4 e2 a1 b3 c4 d5 e2 a1 b5 c3 d4 e2 a1 b5 c4 d3 e2

Any other formations would have already been used, justshifted to the right.
D) The equation to find how manydifferent arrangements there are uses a technique calledfactorial (!)
The equation is:number of seating arrangements = (n-1)! Factorial means, the number * itself -1 and so on until youget to one (ex. 5! = 5*4*3*2*1 = 120, 4! = 4*3*2*1 = 24)

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