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If there are 27 people in a class how do you work out how many different ways can they line up?
27!
How many ways can 3 people stand in a line?
SixIf only the order is interesting (not the direction that they are oriented) then In the first place there can be any of the three, in the second place there can be either of the two left and then the last place is a given so: 3 * 2 * 1 = 6Six different orders for three people standing in a line.If their direction is also interesting to take into account (e.g. the middle person facing north while the others face east) then you have to know how many different directions and if standing on their heads counts as different etc.
If points M N O and P are arranged in such a way that three of them line how many lines are there?
The three points on a line form ONE line; the fourth point forms THREE additional lines, one with each of the first three points. So, four in total.
How many ways can 6 people line up in a straight line to take a picture?
720
Does every line have an infinite number of lines perpendicular to the given line?
Yes. There can be a line perpendicular to the given line at every point on it, and you know how many different points there are on it ...
