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We-have-2-red-and-1-black-tokens-We-want-to-dispose-them-on-9-places-of-this-checker-board-1-What-the-number-of-possibilities-to-dispose-these-3-tokens-on-these-9-places-2-What-it-is-the-number-of




Question Number 102101 by mathocean1 last updated on 06/Jul/20
We have 2 red and 1 black tokens.  We want to dispose them on 9 places  of this checker−board.  1)What the number of possibilities   to dispose these 3 tokens on these  9 places.  2)What it is the number of possibilities  to dispose these 3 tokens  like that:  a) one red token on one black place.  b)two red tokens on black places.  c)zero red token one black places.
$${We}\:{have}\:\mathrm{2}\:{red}\:{and}\:\mathrm{1}\:{black}\:{tokens}. \\ $$$${We}\:{want}\:{to}\:{dispose}\:{them}\:{on}\:\mathrm{9}\:{places} \\ $$$${of}\:{this}\:{checker}−{board}. \\ $$$$\left.\mathrm{1}\right){What}\:{the}\:{number}\:{of}\:{possibilities}\: \\ $$$${to}\:{dispose}\:{these}\:\mathrm{3}\:{tokens}\:{on}\:{these} \\ $$$$\mathrm{9}\:{places}. \\ $$$$\left.\mathrm{2}\right){What}\:{it}\:{is}\:{the}\:{number}\:{of}\:{possibilities} \\ $$$${to}\:{dispose}\:{these}\:\mathrm{3}\:{tokens}\:\:{like}\:{that}: \\ $$$$\left.{a}\right)\:{one}\:{red}\:{token}\:{on}\:{one}\:{black}\:{place}. \\ $$$$\left.{b}\right){two}\:{red}\:{tokens}\:{on}\:{black}\:{places}. \\ $$$$\left.{c}\right){zero}\:{red}\:{token}\:{one}\:{black}\:{places}. \\ $$$$ \\ $$
Commented by mathocean1 last updated on 06/Jul/20
Answered by PRITHWISH SEN 2 last updated on 06/Jul/20
  1)C_3 ^9   2.  a)C_1 ^3 ×C_1 ^6 ×C_1 ^7   b)C_2 ^3 ×C_1 ^7   c)C_2 ^6 ×C_1 ^7
$$ \\ $$$$\left.\mathrm{1}\right)\mathrm{C}_{\mathrm{3}} ^{\mathrm{9}} \\ $$$$\mathrm{2}. \\ $$$$\left.\mathrm{a}\right)\mathrm{C}_{\mathrm{1}} ^{\mathrm{3}} ×\mathrm{C}_{\mathrm{1}} ^{\mathrm{6}} ×\mathrm{C}_{\mathrm{1}} ^{\mathrm{7}} \\ $$$$\left.\mathrm{b}\right)\mathrm{C}_{\mathrm{2}} ^{\mathrm{3}} ×\mathrm{C}_{\mathrm{1}} ^{\mathrm{7}} \\ $$$$\left.\mathrm{c}\right)\mathrm{C}_{\mathrm{2}} ^{\mathrm{6}} ×\mathrm{C}_{\mathrm{1}} ^{\mathrm{7}} \\ $$

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