1.Thuy delivers 6 letters to 6 houses.what is the probability she delivers them all incorrectly?
2. when flipping a fair coin, what is the probability four heads appear?
3. five boys and five girls sit around a circular table. what is the probability they sit alternately?
4. eight keys are on a circular keychain. what is the proabbility the green and gold keys are adjacent to each other?
1. We are counting the derangements of 6, so the probability is 265/720 = 53/144
2. (1/2)^4 = 1/16
3. There is only two ways to seat them: BG BG BG BG BG or GB GB GB GB GB. This can happen in 2 * 5! = 240 ways.
Because the table is circular, we have 10!/10 = 362880 total ways to seat them, and the probability is 240/362880 = 1/1512. (i'm a bit unsure of this)
4. Count the cases where the keys are together: GG _ _ _ _ _ _ (underscores represent other keys) If we count GG as a single block, there are 2 * 7! ways out of a total 8! ways, which is 1/4.