# How-many-ways-can-this-be-done-if-you-distribute-25-identical-pieces-of-candy-among-five-children-

Question Number 134482 by benjo_mathlover last updated on 04/Mar/21
$$\\$$How many ways can this be done if you distribute 25 identical pieces of candy among five children?
Commented by mr W last updated on 04/Mar/21
$${you}'{ll}\:{get}\:{problem}\:{if}\:{you}\:{don}'{t}\:{give} \\$$$$\left.{each}\:{child}\:\mathrm{5}\:{pieces}!\::\right) \\$$$$\\$$$${mathematically}\:{to}\:{get}\:{an}\:{unique} \\$$$${answer}\:{you}\:{must}\:{specify}\:{if}\:{each} \\$$$${child}\:{may}\:{get}\:{nothing}\:{or}\:{must}\:{get} \\$$$${at}\:{least}\:{one}\:{piece}.\:{if}\:{i}\:{were}\:{you},\:{i}'{ll} \\$$$${add}\:{if}\:{each}\:{child}\:{must}\:{get}\:{at}\:{least} \\$$$${two}\:{pieces}. \\$$
Commented by benjo_mathlover last updated on 04/Mar/21
$$\\$$hello sir, that's the problem written in the book no other explanation
Commented by mr W last updated on 04/Mar/21
$${then}\:{it}'{s}\:{assumed}\:{that}\:{a}\:{box}\:\left({here}\:{a}\right. \\$$$$\left.{child}\right)\:{may}\:{be}\:{empty}.\:{in}\:{this}\:{case} \\$$$${there}\:{are}\:{C}_{\mathrm{4}} ^{\mathrm{25}+\mathrm{4}} =\frac{\mathrm{29}!}{\mathrm{25}!\mathrm{4}!}=\mathrm{23751}\:{ways}. \\$$
Commented by mr W last updated on 04/Mar/21
$${if}\:{each}\:{child}\:{must}\:{get}\:{at}\:{least} \\$$$${two}\:{pieces},\:{then}\:{we}\:{have}\:{in}\:{fact}\:{only} \\$$$$\mathrm{15}\:{pieces}\:{to}\:{distribute},\:{there}\:{are} \\$$$${C}_{\mathrm{4}} ^{\mathrm{15}+\mathrm{4}} =\mathrm{3876}\:{ways}. \\$$
Commented by benjo_mathlover last updated on 04/Mar/21
$$\mathrm{ok}\:\mathrm{sir}.\:\mathrm{thanks} \\$$