In how many ways can 5 persons occupy 3 vacant seats?

To find: number of arrangements of 5 people in 3 seats.

 Consider three seats $\underline{A} \underline{B} \underline{C}$

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.