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
