Question Number 121829 by bemath last updated on 12/Nov/20
Answered by mr W last updated on 12/Nov/20
$${no}\:{empty}:\:\mathrm{3}!=\mathrm{6} \\ $$$${one}\:{empty}:\:\mathrm{3}×\mathrm{2}×\mathrm{3}=\mathrm{18} \\ $$$$\Rightarrow{totally}\:\mathrm{24} \\ $$
Commented by bemath last updated on 12/Nov/20
$${why}\:{sir}? \\ $$
Commented by mr W last updated on 12/Nov/20
$${no}\:{box}\:{empty}: \\ $$$${to}\:{arrange}\:{three}\:{balls}\:{there}\:{are}\:\mathrm{3}!\:{ways}. \\ $$$$ \\ $$$${one}\:{box}\:{empty}: \\ $$$${to}\:{select}\:{the}\:{empty}\:{box}\:{there}\:{are}\:\mathrm{3} \\ $$$${ways}.\:{to}\:{select}\:{the}\:{remaining}\:{box} \\ $$$${which}\:{contains}\:{one}\:{ball}\:{there}\:{are}\:\mathrm{2} \\ $$$${ways}.\:{to}\:{select}\:{one}\:{ball}\:{to}\:{put}\:{it}\:{into} \\ $$$${this}\:{box}\:{there}\:{are}\:\mathrm{3}\:{ways}. \\ $$$$\Rightarrow\mathrm{3}×\mathrm{2}×\mathrm{3}=\mathrm{18}\:{ways}. \\ $$
Commented by bemath last updated on 12/Nov/20
$${thank}\:{you}\:{sir}\: \\ $$