Seven people (A, B, C, D, E, F, G) are lining up to enter a museum. 1. How many ways are there to line up the seven people if B is somewhere before G, although not necessarily immediately before? 2. How many ways are there to line up the seven people if E, F and G are next to each other? 3. How many ways are there to line up the seven people if C must be next to E but D and F can not be next to each other? 4. How many ways are there to line up the seven people if C is next to E? 5. How many ways are there to line up the seven people if A must be somewhere before. B, B must be somewhere before C, and C must be somewhere before D? (Note: some where before does not necessarily mean they must be next to each other)
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INTRODUCTION
Combinations refer to the choice of things without respect to order, whereas permutations refer to the arranging of elements in a certain order. An arrangement of items in a particular order is referred to as a permutation. A combination is a collection of items chosen randomly.
Given details: Seven people are lining up to enter a museum.
To determine: 1. The number of ways are there to line up the seven people if B is somewhere before G, although not necessarily immediately before.
2. The number of ways there to line up the seven people if E, F, and G are next to each other.
3. The number of ways are there to line up the seven people if C must be next to E but D and F can not be next to each other.
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