Question Number 163283 by greg_ed last updated on 05/Jan/22
$$\mathrm{hi}\:! \\ $$ We store 5 objects in three discernible drawers. Suppose that the different ways of carrying out these arrangements are equally probable, calculate the probability that one of the 3 drawers contains at least 3 objects.\\n
Commented bymr W last updated on 05/Jan/22
$${identical}\:{objects}? \\ $$ $${identical}\:{drawers}? \\ $$ $${may}\:{a}\:{drawer}\:{be}\:{empty}? \\ $$
Answered by mr W last updated on 06/Jan/22
$$\mathrm{0}+\mathrm{0}+\mathrm{5}\:\ast \\ $$ $$\mathrm{0}+\mathrm{1}+\mathrm{4}\:\ast \\ $$ $$\mathrm{0}+\mathrm{2}+\mathrm{3}\:\ast \\ $$ $$\mathrm{1}+\mathrm{1}+\mathrm{3}\:\ast \\ $$ $$\mathrm{1}+\mathrm{2}+\mathrm{2} \\ $$ $${total}:\:\mathrm{5}\:{ways} \\ $$ $${at}\:{least}\:\mathrm{3}\:{in}\:{one}\:{drawer}:\:\mathrm{4}\:{ways} \\ $$ $${p}=\frac{\mathrm{4}}{\mathrm{5}}=\mathrm{80\%} \\ $$