Yahoo Answers: Answers and Comments for Statistics  Permutations & Combinations Confirm Solution/Help? [Mathematics]
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From Tessa
enCA
Fri, 17 Jan 2020 08:30:28 +0000
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Yahoo Answers: Answers and Comments for Statistics  Permutations & Combinations Confirm Solution/Help? [Mathematics]
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https://ca.answers.yahoo.com/question/index?qid=20200117083028AAeFQJk
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From Puzzling: Let me go through all the parts.
PART 1:
Fro...
https://ca.answers.yahoo.com/question/index?qid=20200117083028AAeFQJk
https://ca.answers.yahoo.com/question/index?qid=20200117083028AAeFQJk
Thu, 13 Feb 2020 04:08:00 +0000
Let me go through all the parts.
PART 1:
From the 30 IPAs, pick 4 > C(30,4)
From the 6 Lagers, pick 4 > C(6,4)
Answer:
C(30,4) * C(6,4)
PART 2:
We only care about one particular selection of 8 beers.
We have two alternating patterns (ILILILIL or LILILILI).
For the 4 IPAs we have 4! ways to arrange them.
Similarly for the 4 Lagers we have 4! ways to arrange them.
Answer:
2 * 4! * 4!
PART 3:
Once we place a beer, that will determine the alternating pattern. For example, if we put an IPA in position 3, then the other IPAs must go in the remaining odd positions. And if the first IPA goes in an even position, the other IPAs must go in an even position.
Let's place the two pink beers first.
If All Together Now goes on an end (2 choices), then there are 3 choices for where Hot Pink goes > 2 * 3 = 6
If All Together Now goes in a middle spot (6 choices), then there are 2 choices for where Hot Pink goes > 6 * 2 = 12
So there are 18 ways to place the special pink beers. Then there are 3! ways to place the other IPAs and 3! ways to place the other Lagers.
Answer:
18 * 3! * 3!
PART 4:
Again, let's place the special pink beers first.
If All Together Now is placed in positions 1, 2 or 3, then there are 2 places where Hot Pink can go on the right side > 3 * 2 = 6
If All Together Now is placed in position 4, then there is 1 place it can go on the right side (position 7) 1 * 1 = 1
So there are 7 ways to place the special pink beers where All Together Now is on the left and Hot Pink is on the right. Again we have 3! * 3! ways to place the other beers.
Answer:
7 * 3! * 3!