[Probability] Seating arrangement & Selection

PROBLEM 1

7 people sit in a row, and 2 of them want to sit together, in how many ways can they be arranged?

ATTEMPTED SOLUTION:

6! x 2 = 1440

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PROBLEM 2

7 people sit in a row, and 2 of them do not want to sit together, in how many ways can they be arranged?

ATTEMPTED SOLUTION:

No ideas

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PROBLEM 3

7 people sit in a circular formation, but 2 of them do NOT want to sit together, in how many ways can they be arranged?

ATTEMPTED SOLUTION

No ideas

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PROBLEM 4

There are 10 red & 6 blue marbles in a bag. You pick 2 of them at the same time.

In how many ways can you pick 2 marbles of the same color? Different colors?

ATTEMPTED SOLUTION:

Same colors: 10/16 x 9/15 + 6/16 x 5/15

Different colors: 10/16 x 6/16 + 9/15 x 5/15