To find: number of arrangements of 5 people in 3 seats.
Consider three seats A B C
Now, place A can be occupied by any 1 person out of 5.
Then place B can be occupied by any 1 person from remaining 4 and for C there are 3 people to occupy the seat.
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 5 different objects in 3 places is
P(5,3) = \(\frac{5!}{(5-3)!}\)
= \(\frac{5!}{2!}\) = \(\frac{120}{2}\) = 60.
Therefore, the number of possible solutions is 60.
