Question 221650: This problem stumps me..can u please explain how to work it??
The producer of All Things Considered, a radio-news program on NPR, has 4 in-depth and 8 short news stories for broadcast during the next two hours. The producer must arrange the in-depth and short stories by starting with an in-depth story followed by two short stories, and then another in-depth story and two short stories until all 12 stories have been aired. How many arrangements for the broadcast are possible?
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! The producer of All Things Considered, a radio-news program on NPR, has 4 in-depth and 8 short news stories for broadcast during the next two hours.
The producer must arrange the in-depth and short stories by starting with an in-depth story followed by two short stories, and then another in-depth story and two short stories until all 12 stories have been aired.
How many arrangements for the broadcast are possible?
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1st segment: 4 ways
2nd/3rd segment: 8*7 ways
4th segment: 3 ways
5th/6th segment: 6*5 ways
7th: 2 ways
8th/9th segment: 4*3 ways
10th: 1 way
11th/12th: segment: 2*1
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Total # of ways: 4!*8! = 967680
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Cheers,
Stan H.
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