SOLUTION: 11. A group of 5 boys took their girlfriends with them to a seaside picnic right after their quiz in QUAMETH. a. They arrived at the resort late in the afternoon and decided t

Question 1145536: 11. A group of 5 boys took their girlfriends with them to a seaside picnic right after their quiz in QUAMETH.
a. They arrived at the resort late in the afternoon and decided to rent a large cottage having three rooms with the following maximum allowable number of occupants per room: 5 persons in the Royal Suite; 4 persons in the De Luxe Suite; and 3 persons in the Standard Suite. Following their parents’ strict advice, the girls did not sleep in the same room where the boys did. How many possible ways can the vacationists sleep for the night?
b. The following morning, they went to the kitchen hall and gathered around a circular table to eat their breakfast. How many ways can they sit around the table if the couples are to be sitting together?
c. They formed a committee of four persons to prepare lunch. One of the vacationists was a good cook and it was decided that she should be on the committee. Two other girls, however, who are always quarreling, should not be on the committee both at the same time. How many possible committees are there?
d. Late in the afternoon, to liven up their merienda, they decided to put up a contest. They have 1st, 2nd and 3rd prizes at stake. How many ways can these prizes be won?
e. They had to leave before dark so they started to pack up their things. To bid each other farewell, they shook hands with each other. Of course, the boys did not shook hands with their own girlfriends; instead they kissed them goodbye. How many handshakes were there assuming that two persons shook hands with each other only once?
Answer by ikleyn(52778) (Show Source): You can put this solution on YOUR website!
.

I will answer SELECTED positions only.

(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)   = 10 handshakes boys with boys   PLUS

      = 10 handshakes girls with girls  PLUS

     5*4  = 20 handshakes boys with girls = 10 + 10 + 20 = 40 handshakes, in all.

I hope other tutors will answer remaining positions.

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