In how many ways can 7 people line up at a ticket window of a cinema hall?

To find: number of arrangements of 7 people in a queue.

Here there are 7 spaces to be occupied by 7 people.

Therefore 7 people can occupy first place.

Similarly, 6 people can occupy second place and so on.

Lastly, there will be a single person to occupy the 7 positions.

Formula:

Number of permutations of n distinct objects among r different places, where repetition is not allowed, is

P(n,r) = n!/(n-r)!

Therefore, permutation of 7 different objects in 7 places is

P(7,7) =

= = = 5040.

Therefore, the number of possible ways is 5040