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Question Number 154942 by Tawa11 last updated on 23/Sep/21

Answered by prakash jain last updated on 23/Sep/21

$$\mathrm{You}\mathrm{need}\mathrm{to}\mathrm{take}16\mathrm{steps},8\mathrm{down}$$$$\mathrm{and}8\mathrm{right}.$$$$\mathrm{The}\mathrm{problem}\mathrm{is}\mathrm{simply}\mathrm{choosing}$$$$8\mathrm{down}\mathrm{steps}\mathrm{among}\mathrm{available}16$$$$\mathrm{position}.$$$$\mathrm{ans}:{}^{16}{\mathrm{C}}_8$$$$\mathrm{Ex}:$$$$----------------$$$$-\mathrm{DDDDDDDD}-------$$$$\mathrm{Once}\mathrm{you}\mathrm{choose}8\mathrm{down}\mathrm{steps}$$$$\mathrm{remaining}8\mathrm{are}\mathrm{right}$$

Commented by Tawa11 last updated on 24/Sep/21

$$\mathrm{God}\mathrm{bless}\mathrm{you}\mathrm{sir}$$

Answered by mr W last updated on 23/Sep/21

$$wecanonlygorightordown.$$$$wehavetotally16steps,8timesright$$$$and8timesdown.toarrange8times$$$$rightand8timesdown,thereare$$$$\frac{16!}{8!8!}=12870ways.$$

Commented by Tawa11 last updated on 24/Sep/21

$$\mathrm{God}\mathrm{bless}\mathrm{you}\mathrm{sir}.$$

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