Question Number 102101 by mathocean1 last updated on 06/Jul/20
$${We}\:{have}\:\mathrm{2}\:{red}\:{and}\:\mathrm{1}\:{black}\:{tokens}. \\ $$$${We}\:{want}\:{to}\:{dispose}\:{them}\:{on}\:\mathrm{9}\:{places} \\ $$$${of}\:{this}\:{checker}−{board}. \\ $$$$\left.\mathrm{1}\right){What}\:{the}\:{number}\:{of}\:{possibilities}\: \\ $$$${to}\:{dispose}\:{these}\:\mathrm{3}\:{tokens}\:{on}\:{these} \\ $$$$\mathrm{9}\:{places}. \\ $$$$\left.\mathrm{2}\right){What}\:{it}\:{is}\:{the}\:{number}\:{of}\:{possibilities} \\ $$$${to}\:{dispose}\:{these}\:\mathrm{3}\:{tokens}\:\:{like}\:{that}: \\ $$$$\left.{a}\right)\:{one}\:{red}\:{token}\:{on}\:{one}\:{black}\:{place}. \\ $$$$\left.{b}\right){two}\:{red}\:{tokens}\:{on}\:{black}\:{places}. \\ $$$$\left.{c}\right){zero}\:{red}\:{token}\:{one}\:{black}\:{places}. \\ $$$$ \\ $$
Commented by mathocean1 last updated on 06/Jul/20
Answered by PRITHWISH SEN 2 last updated on 06/Jul/20
$$ \\ $$$$\left.\mathrm{1}\right)\mathrm{C}_{\mathrm{3}} ^{\mathrm{9}} \\ $$$$\mathrm{2}. \\ $$$$\left.\mathrm{a}\right)\mathrm{C}_{\mathrm{1}} ^{\mathrm{3}} ×\mathrm{C}_{\mathrm{1}} ^{\mathrm{6}} ×\mathrm{C}_{\mathrm{1}} ^{\mathrm{7}} \\ $$$$\left.\mathrm{b}\right)\mathrm{C}_{\mathrm{2}} ^{\mathrm{3}} ×\mathrm{C}_{\mathrm{1}} ^{\mathrm{7}} \\ $$$$\left.\mathrm{c}\right)\mathrm{C}_{\mathrm{2}} ^{\mathrm{6}} ×\mathrm{C}_{\mathrm{1}} ^{\mathrm{7}} \\ $$