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anonymous
 5 years ago
There are two rows of seats with three sidebyside seats in each row. Two little boys, two little girls, and two adults sit in the six seats so that neither little boy sits to the side of either little girl. In how many different ways can these six people be seated?
OPTIONS
1) 48
2) 128
3) 192
4) 176
anonymous
 5 years ago
There are two rows of seats with three sidebyside seats in each row. Two little boys, two little girls, and two adults sit in the six seats so that neither little boy sits to the side of either little girl. In how many different ways can these six people be seated? OPTIONS 1) 48 2) 128 3) 192 4) 176

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mattfeury
 5 years ago
Best ResponseYou've already chosen the best response.0I am inclined to think: \[2!^3 * 3! = 48 \]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0can we think in linear way??

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0how did you get that answer

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0or kindely explain how u did?

mattfeury
 5 years ago
Best ResponseYou've already chosen the best response.0if you a have of couple (2 people), you can arrange them in 2! ways. 2! = 2 * 1 = 2 if you have three couples in 3 rows, then they can be sat = \[2! * 2! * 2!\]

mattfeury
 5 years ago
Best ResponseYou've already chosen the best response.0but! it can be: couple1 couple2 couple3 couple3 couple2 couple1 etc... so we can arrange the 3 couples in 3! ways.

mattfeury
 5 years ago
Best ResponseYou've already chosen the best response.0so basically we have 6 seats. but first we simply that to three rows. we have three rows. a couple per row. there are 3! ways to arrange this. in each row, each couple can be arranged 2! ways. Since this is the case for each of the three rows, it is 2! * 2! * 2! multiplying all these possibilities together: 2! * 2! * 2! * 3! = 48

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0you're treating the two boys as a couple?

mattfeury
 5 years ago
Best ResponseYou've already chosen the best response.0ah yeah sorry. i was thinking of a similar problem with 3 couples. it is the same principle though. 3 sets of 2 individuals (in this case: boys, girls, adults).

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0but you can rearrange the couples

mattfeury
 5 years ago
Best ResponseYou've already chosen the best response.0yes. you can arrange the couples between the three rows. thus the 3!

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0we have two rows _ _ _ _ _ _

mattfeury
 5 years ago
Best ResponseYou've already chosen the best response.0ah i am so wrong. you are right.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0yes thats what m thinking .. how to solve its definitely not circular and I doubt on Linear permutation

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0thats why i got confused about your answer

mattfeury
 5 years ago
Best ResponseYou've already chosen the best response.0heh sorry. i misread the question :(. that's what i get for skimming.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0i will forgive you if you help me with my question, brb

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0but go ahead and try to answer

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0so you solved the question, 3 rows, boy cant sit next to girl?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0so i guess is it correct?? B1 B2 A1 6 WAYS G1 G2 A2 6 WAYS ie, TOTAL =36 ways

mattfeury
 5 years ago
Best ResponseYou've already chosen the best response.0there is another set of cases: B1 A1 G1 B2 A2 G2

mattfeury
 5 years ago
Best ResponseYou've already chosen the best response.0B1 A1 G1 = 2 ways to arrange B2 A2 G2 = 2 ways to arrange

mattfeury
 5 years ago
Best ResponseYou've already chosen the best response.0better: B1 A1 G1 = 4 * 3 to arrange (you have a set of {b1, b2, g1, g2} and you have 4 and 3 options for the end) B2 A2 G2 = 2 * 1 ways to arrange

mattfeury
 5 years ago
Best ResponseYou've already chosen the best response.012 * 2 * 2 (another 2 to choose between the A's) = 48 for that case.

mattfeury
 5 years ago
Best ResponseYou've already chosen the best response.0times another 2 to account for being able to switch the rows: r1, r2 or r2, r1

mattfeury
 5 years ago
Best ResponseYou've already chosen the best response.0= 96 for that case. you'll have to + this to the possibilities for the other case

mattfeury
 5 years ago
Best ResponseYou've already chosen the best response.0i may be wrong though. i can't seem to figure out the other case to where it adds to an answer :( 96 + (2 * 2 * 2 * 2) = 112?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0I am also confused dear :)

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0can it be like? B A G B A G G A B G A B B B A G G A G G A B B A A B B A G G A G G A B B Each case can be arranged in 8 ways , i.e. Boys  2! , Gals  2! , adults  2! Hence 6 * (2*2*2) = 48 Option 1

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0hi cantorset .. u ther??

nowhereman
 5 years ago
Best ResponseYou've already chosen the best response.0The only possible cases are, if the girls sit on different rows, that the parents sit in the middle seats and the boys on the other sides. If the girls sit on the same row the third seat must be occupied by a parent and there is no further restriction on the other row. So you get for the number of constellations: In the first case 4*2!*2!*2! = 32 and in the second case 2*3*3*2!*2!*2! = 144, that means there are 176 possibilties.

nowhereman
 5 years ago
Best ResponseYou've already chosen the best response.0need more explanation?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0yes i do, i got the same answer but i didnt get your 2x3x3x2! , etc

nowhereman
 5 years ago
Best ResponseYou've already chosen the best response.02 because the girls can either sit in the first or in the second row 3 because you can choose any seat in that row for the parent 3 because you must choose one seat in the other row where the second parent sits 2!*2!*2! always because it doesn't matter if you interchange the 2 girls / boys / parents with each other.
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