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?
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 <--------
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 <--------