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  • Examtple 1 There are 2 buses (B), 3 trains $T$ ) and 5 planes (F) avalible to iravel from Mumbal (MLM) io Dehin iDEL). There are 6 plares available from DEE io tondon ILON and 7 plates available fo

Examtple 1 There are 2 buses (B), 3 trains $T$ ) and 5 planes (F) avalible to iravel from Mumbal (MLM) io Dehin iDEL). There are 6 plares available from DEE io tondon ILON and 7 plates available foom LON io New York iNY, Alsc. there are 8 direct planes from ALLM io LON, 9 divect plares from DEL to NY and 10 direct planes from MLNd to Nr.
Now, answer the following question,
in how many ways can a person travel from
(i)\mathrm{MUM} \rightarrow DEL \text{ and }(ii)\mathrm{MUM} \rightarrow \mathrm{NY} ?
 

Option: 1


146,576


Option: 2

142 525


Option: 3

120 ,512

 


Option: 4

none of these


Answers (1)

best_answer

(i) \mathrm{MUM} \rightarrow \mathrm{DEL}
Numbes of ways to go from \mathrm{MUM} \rightarrow \mathrm{DEL}=3+2+5=10

(ii)\mathrm{NUM} \rightarrow \mathrm{NY}
We can go from MUM to NY in one of the following two ways
a) By direct journey (10 ways)
b) By break journey (566 ways)
Brakk joumey can again be done in two ways
1. By teking a single break
\begin{aligned} & \mathrm{MLM} \rightarrow \mathrm{DEL} \rightarrow \mathrm{NY}=10 \times 9=90 \text { ways } \\ & \mathrm{MUM} \rightarrow \mathrm{LON} \rightarrow \mathrm{NY}=8 \times 7=56 \text { ways } \end{aligned}
\therefore Number of ways to travel by just one break =90+56 =146 \ ways

2. By taking 2 breaks


\therefore Number of ways to go from MUM $\rightarrow$ NY by taking 2 breaks
=10 \times 6 \times 7=420 \text { ways }
  \therefore Number of ways to travel from NUM \rightarrow NY by break joumey
=420+146=566 \text { ways }
\therefore Roquired number of ways =566+10=576 \ ways

Posted by

Devendra Khairwa

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