Question 1145536
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            I will answer SELECTED positions only.



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(b) 2*(5-1)! = 2*4! = 2*24 = 48 ways  (considering circular permutations only, traditionally for such kind of problems)



(d) If prizes are distinguishable (as it follows from the context), then the answer is 10*9*8 = 720 ways.


(e)  {{{(5*4)/2}}} = 10 handshakes boys with boys   PLUS

     {{{(5*4)/2}}} = 10 handshakes girls with girls  PLUS

     5*4  = 20 handshakes boys with girls = 10 + 10 + 20 = 40 handshakes, in all.
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I hope other tutors will answer remaining positions.