3 couples seated randomly around a round table. What's the chance 1 or more of the couples will be together? - couples 1 candid hd
3 couples. Are randomly seated around a round table. What is the probability that one or more couples can sit together - the husband of the woman to the left or right, never mind.
Thursday, February 4, 2010
Couples 1 Candid Hd 3 Couples Seated Randomly Around A Round Table. What's The Chance 1 Or More Of The Couples Will Be Together?
2 comments:
First, there are n (-1)! Ways to arrange for n people in a circle. There are (6-1)! = 120 ways to sit these people.
Not likely to find couples together, then subtract 1 from it.
Definition of a person. Your partner can right seat in the place left or right. Turn left. The other couples can in (2x2x2) are organized, ie. This also applies to the right. (2x) There are 2x2x2x2 = 16 possibilities for now. Your partner can also sit in front. There are opportunities to sit, 2x2x2x2 = 16 remaining couples can. In total there are 32 possibilities. 32/120 =. 27. Thus, the probability is at least a couple together, 73 This solution is consistent with simulation results.
EXTRA:
Chance more accurate.
It was a couple together (2x). Other couples can have a seat away. You can change places. (2x2) to exchange seats with another pair (2x). It 2x2x2x2 = 16 positions, when a couple has been corrected. The setting of the other seats completely different form, is the total number of seats with a pair of 16 * 3 = 48 possible. The probability is 48/120 =. 4. \\ \\ \\ \\ \\ \\ \\ \\ U0026lt;br>
Probability that exactly two pairs.
Fix a pair (2x) and the combination of the other pair, for example, B and (2x). B can sit in front of one, because if they sit side by side will be 3 couples sit together. The remaining two seats can go (2x). We choose A and B 3x in three different ways (). Thus, the number of places is possible 2x2x2x3 = 24 The probability is 24/120 =. 2.
Probability that exactly three pairs. Three couples seated. None of them can change place (3x ^ 2). Just to keep (3-1 = 2), as Article 3 in a circle. Thus it is possible to sit (2 ^ 3x2 = 16). The probability is 16/120 =. 13.
The total number of seats 32 48 24 16 = 120.
at least one partner is as follows: Put this couple ... 4 people have to organize themselves to ... Torque can be changed,
Number of ways = 4! x 2 = 48
at least two couples who are together: It was a couple ...
There are 3 units to organize ... Couples can their body
Number of ways = 3! x 2 x 2 = 24
3 pairs together
Number of ways 2x2x2x2 = = 16
Number of ways in which at least a couple sitting next to = 48 - 24 + 16 = 40
Total forms of organization of 6 people in a circle ... = 5! = 120
Thus, the total probability = 40/120
= 1 / 3
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