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This is a good example of a very poorly specified question. There are four correct answers which depend on conditions which are unspecified in the question. The chairs can be in a line or around a table (in a crude circle); and in each case you can be interested only in who is sitting next to whom (or a vacant chair) but not really interested on whether it is to the right or left (so that mirror images are counted as the same).
- chairs are in a line and the direction does matter, then there are 2520.
- chairs are in a line and the direction does not matter, then there are 1260.
- chairs are in a circle and the direction does matter, then there are 360.
- chairs are in a circle and the direction does not matter, then there are 180.
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How many ways can 8 people sit in 5 chairs?
8x7x6x5x4= 6720
What do people sit on?
chairs
How many ways are there to seat 25 people?
There are about 2 sensible reasons. You get 25 chairs tell the 25 people to sit. Tell them to sit on the floor.Answer:25 people can be seated in 25! ways (25! is factorial 25, or 25x24x22x21 ....x3x2x1) as the first chair can be filled in 25 ways, the second in 24, the third in 23 and so on. This comes to 1.5511210043 × 1025 different ways
How many different ways can four people sit in a row if two must sit together?
There are 12 ways.
How many ways can two women and a man sit in a row of five empty chairs if the two women have to sit next to each other?
If the first woman sits at an end, there is only the seat next to her where the second woman can sit. There are 2 such chairs, giving 2 × 1 = 2 possible sittings. If the first woman doesn't sit at the end, the second woman can sit either side of her in one of 2 chairs. There are 5 - 2 = 3 such chairs, giving, 2 × 3 = 6 possible sittings. Thus there are 2 + 6 = 8 possible sitting positions of the women. For each of these there are 3 empty chairs which the man can occupy, Thus there are 8 × 3 = 24 possible ways that 2 women and 1 man can sit on a row of 5 empty chairs if the two women must sit together.
