NIELIT 2017 July Scientist B (IT) - Section B: 14

Question

There are four bus lines between $A$ and $B$; and three bus lines between $B$ and $C$. The number of way a person roundtrip by bus from $A$ to $C$ by way of $B$ will be

• A. $12$
• B. $7$
• C. $144$
• D. $264$

Answer 1

nos of ways fromA to C via B is 4*3=12

Similarly no of ways from C to A via B =3*4=12.

So for round trip nos of ways =12*12=144

Hence the option C is correct.

Answer 2

Number of ways to choose path from $A$ to $B$ = 4C1 

Number of ways to choose path from $B$ to $C$= 3C1

Now during roundtrip

Number of ways to choose path from $C$ to $B$ = 3C1

Number of ways to choose path from $B$ to $A$= 4C1

Total possibe combinations= $4C1 * 3C1 * 3C1 * 4C1 $= $4*3*3*4= 144$

Hence Option C) is correct answer