The number of ways of distributing 500 dissimilar boxes equally among ' 50 ' persons is
The number of ways of distributing 500 dissimilar boxes equally among ' 50 ' persons is
$500 ! /(10 !)^{50} \cdot 50$ !
$500 ! /(50 !)^{10} .10$ !
$500 ! /(50 !)^{10}$
$500 ! /(10 !)^{50}$
Solution
We know that number of ways in which $\mathrm{m} \times \mathrm{n}$ distinct things can be distributed among $\mathrm{n}$ persons.
$
=\frac{(\mathrm{mn}) !}{(\mathrm{m} !)^{\mathrm{n}}}
$
$\therefore$ Number of ways of distributing 500 i.e. $50 \times 10$ dissimilar bones equally among 50 persons.
$
=\frac{500 !}{(10 !) 50}
$