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Question-154942




Question Number 154942 by Tawa11 last updated on 23/Sep/21
Answered by prakash jain last updated on 23/Sep/21
You need to take 16 steps, 8 down  and 8 right.  The problem is simply choosing  8 down steps among available 16  position.  ans:^(16) C_8   Ex:  −−−−−−−−−−−−−−−−  −DDDDDDDD−−−−−−−  Once you choose 8 down steps  remaining 8 are right
$$\mathrm{You}\:\mathrm{need}\:\mathrm{to}\:\mathrm{take}\:\mathrm{16}\:\mathrm{steps},\:\mathrm{8}\:\mathrm{down} \\ $$$$\mathrm{and}\:\mathrm{8}\:\mathrm{right}. \\ $$$$\mathrm{The}\:\mathrm{problem}\:\mathrm{is}\:\mathrm{simply}\:\mathrm{choosing} \\ $$$$\mathrm{8}\:\mathrm{down}\:\mathrm{steps}\:\mathrm{among}\:\mathrm{available}\:\mathrm{16} \\ $$$$\mathrm{position}. \\ $$$$\mathrm{ans}:\:^{\mathrm{16}} \mathrm{C}_{\mathrm{8}} \\ $$$$\mathrm{Ex}: \\ $$$$−−−−−−−−−−−−−−−− \\ $$$$−\mathrm{DDDDDDDD}−−−−−−− \\ $$$$\mathrm{Once}\:\mathrm{you}\:\mathrm{choose}\:\mathrm{8}\:\mathrm{down}\:\mathrm{steps} \\ $$$$\mathrm{remaining}\:\mathrm{8}\:\mathrm{are}\:\mathrm{right} \\ $$
Commented by Tawa11 last updated on 24/Sep/21
God bless you sir
$$\mathrm{God}\:\mathrm{bless}\:\mathrm{you}\:\mathrm{sir} \\ $$
Answered by mr W last updated on 23/Sep/21
we can only go right or down.  we have totally 16 steps, 8 times right   and 8 times down. to arrange 8 times  right and 8 times down, there are  ((16!)/(8!8!))=12870 ways.
$${we}\:{can}\:{only}\:{go}\:{right}\:{or}\:{down}. \\ $$$${we}\:{have}\:{totally}\:\mathrm{16}\:{steps},\:\mathrm{8}\:{times}\:{right}\: \\ $$$${and}\:\mathrm{8}\:{times}\:{down}.\:{to}\:{arrange}\:\mathrm{8}\:{times} \\ $$$${right}\:{and}\:\mathrm{8}\:{times}\:{down},\:{there}\:{are} \\ $$$$\frac{\mathrm{16}!}{\mathrm{8}!\mathrm{8}!}=\mathrm{12870}\:{ways}. \\ $$
Commented by Tawa11 last updated on 24/Sep/21
God bless you sir.
$$\mathrm{God}\:\mathrm{bless}\:\mathrm{you}\:\mathrm{sir}. \\ $$

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