Math Problem... Circular Permutations.
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Math Problem... Circular Permutations.

[From: ] [author: ] [Date: 11-05-10] [Hit: ]
Five men and five women sit around a circular table, men and women alternating. In how many ways can this be done?3. In both a science classroom and history classroom there are 12 desks. In the science class students are seated in circle,......
1. a) In how many ways eight people be seated around a circular table?

b) In how many ways can they seated if Bob and Raj insist on sitting next to each other?


2. Five men and five women sit around a circular table, men and women alternating. In how many ways can this be done?


3. In both a science classroom and history classroom there are 12 desks. In the science class students are seated in circle, and in history class students are seated in a row. Which classroom has the greater number number of seating arrangements?

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in an unnumbered circular seating, there is no fixed refernce point and one person is "lost" in serving as the reference point, so the formula for # of arrangements is (n-1)! as against n! for seating in a row

q3
history class (see above)

q1
a. 7! = 5040<--------

b, take bob & raj as a block [BR] or [RB} + 6 others : 2! *6! = 1440 <--------

q2
seat 5 men in 4! ways in alternating seats. seat
the women can now be seated in their alternating seats in 5! ways
to give 4!*5!= 2880 <--------
1
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