euphrosyne wrote:
Can you please explain your solution once more to me? According to my calculations its 36.
4C2(=6) to choose 2 husbands out of the 4. Now for each husband chosen there are 3 wives that can be paired. So-6*3*2 (cause there are two other husband- wife mixed double combination possible.)
so- 36 answer (c)
After we have chosen the pair of husbands, A and B:
We can choose a and b and we have to pair them as (A,b) and (B,a) -
1 possibility.We can choose one of the wives, a or b, but we have to pair her with the other husband and in addition, we have to choose another partner for the second husband.
This we can do in 2*2 = 4 ways, as there are two possibilities to choose from a and b, then we have 2 possibilities to choose the other wife, c or d -
4 possibilitiesFinally, we can choose the other two wives, c and d, and we have two possibilities to team them up with the men, (A,c), (B,d) or (A,d), (B,c) -
2 possibilities.In conclusion,
for every pair of husbands, we have 1 + 4 + 2 = 7 possibilities to choose their partners for the game.Total number of possibilities 6 * 7 = 42.
Answer D.
Now for each husband chosen there are 3 wives that can be paired. So-6*3*2There are no 6 husbands, but only 4. You should not consider husbands alone.
You should count the possibilities of choosing the wives per chosen pair of husbands, otherwise you cannot keep up with repetitions or you can miss out some possibilities. 6 represents the number of pairs of husbands. Then the number of 3 wives is not correct, as you can see from the above, all four wives can be candidates as partners, depending whom each plays.
If you write down all the possibilities for the pair of husbands A and B, you will get a total of 7 (following the steps described above):
(A,b) (B,a) - 1
(A,b) (B,c); (A,b) (B,d); (A,c) (B,a); (A,d) (B,a) - 4
(A,c) (B,d); (A,d) (B,c) - 2
Or in other words:
1 - two wives stay, but each has to play with the other husband
2 - one wife stays and plays with the other husband, and second husband receives one of the other two wives as a partner
3 - none of the wives stays, the remaining two wives pair up with the already chosen husbands
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PhD in Applied Mathematics
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