Five musicians, two rocket scientists, and an accountant are to be seated around a circular table. How many different arrangements are possible if the musicians must all sit together (in five consecutive seats) and the rocket scientists must sit next to each other? (Two seatings are considered equivalent if one seating can be obtained from rotating the other.)
First, we can seat the musicians. Then we seat the scientsts, then accountant. There are 5! ways to seat the musicians, then 2! ways to seat the scientsts, then 1! way to seat the accountant. Then we divide by 8, so there are 5!*2!*1!/8 = 30 ways to seat everyone.
5 musicians, all together, 5! ways if each scientist is considered an individual
2 scientists, all together, 2 ways if classed as individuals
2*5!*2 = 4*5! = 480 ways
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