Question

A crew of an eight oar boat has to be chosen out of $11$ men five of whom can row on stoke side only, four on the bow side only and the remaining two on either side. How many different selections can be made?

• A. $145$
• B. $150$
• C. $244$
• D. $640$

Answer 1

The correct option is A $145$

$a⟶$ left $b⟶$ right

Case : 1 We use $2$ of them

(a) ${}^5{C}_2{\times }^4{C}_4=10(2,0)$

(b) ${}^5{C}_4{\times }^4{C}_2=30(0,2)$

(c) ${}^5{C}_3{\times }^4{C}_3=40(1,1)$

Case : 2 We use one of them

(a) ${}^5{C}_3{\times }^4{C}_4=10(1,0)$

(b) ${}^5{C}_4{\times }^4{C}_3=20(0,1)$

There are two ways to choose

$\Rightarrow$ There are $60$ possiblities

Case : 3 We use zero of them

${}^5{C}_4{\times }^4{C}_0=5$

$\Rightarrow$ Total Possiblities $=140+5$

$=145$