Question 1110068: Hello, I need help to solve the problem.
A school dance committee is made up of 3 freshman, 2 sophomores, 3 juniors, and 3 seniors.
How many ways are there to sit the committee in a row at a meeting if the students must sit together by grade?
How many ways are there to sit the committee in a row at a meeting if the freshman,sophomores, and juniors must sit by grade, but the seniors can sit wherever they want?
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! Hello, I need help to solve the problem.
A school dance committee is made up of 3 freshman, 2 sophomores, 3 juniors, and 3 seniors.
How many ways are there to sit the committee in a row at a meeting if the students must sit together by grade?
group arrangements:: 4! = 24 ways
within group arrangements:: 3!*2!*3!*3! = 6*2*6*6 = 432
Ans: 24*432 = 10368 ways
How many ways are there to sit the committee in a row at a meeting if the freshman,sophomores, and juniors must sit by grade, but the seniors can sit wherever they want?
grade 3! = 6
group arrangements:: 3!*2!*3! = 6*2*6 = 72
seniors filling 7 in-between positions plus 2 end positions
add 3!*10C3 = 6*120
Ans: 6*6*120 = 4320
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Cheers,
Stan H.
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