Question:
In How many ways can 4 people be seated in a row containing 5 seats?
Solution:
To find : Number of ways in which 4 people can be seated in a row containing 5 seats.
The possible number of ways in which 4 people be seated in a row containing 5 seats $={ }^{7} \mathrm{P}_{4}$ (There are 5 places to be filled with 4 persons where arrangement doesn't matter.)
${ }^{7} \mathrm{P}_{4}=\frac{7 !}{(7-4) !} \ldots\left({ }^{\mathrm{n}} \mathrm{P}_{\mathrm{r}}=\frac{n !}{(n-r) !}\right)$
$=\frac{7 !}{3 !}$
$=7 \times 6 \times 5 \times 4$
$=840$