Question:
In how many ways can 7 people line up at a ticket window of a cinema hall?
Solution:
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
$P(7,7)=\frac{7 !}{(7-7) !}$
$=\frac{7 !}{0 !}=\frac{5040}{1}=5040$
Therefore, the number of possible ways is 5040