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Standard VI

Mathematics

Word Problems

There are 6...

Question

There are $6$ roads between $A$ and $B$ and $4$ roads between $B$ and $C$ .
(i) In how many ways can one drive from $A$ to $C$ by way of $B$ ?
(ii) In how many ways can one drive from $A$ to $C$ and back to $A$ , passing through $B$ on both trips?

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Solution

$6$ roads between A and B
$4$ roads between B and C
(i) A to C via B
A to B $6$ ways, B to C $4$ ways
$\Rightarrow$ A to C via B $= 6 \times 4 = 24$
(ii) A to C via B
C to A via B
A _ B _ C _ B _ A
$6$ $4$ $4$ $6$
No. of ways $= 6 \times 4 \times 4 \times 6 = 24 \times 24 = 576$ .

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There are 6 roads between A and B and 4 roads between B and C.(i) In how many ways can one drive from A to C by way of B?(ii) In how many ways can one drive from A to C and back to A, passing through B on both trips?

6 roads between A and B4 roads between B and C(i) A to C via BA to B 6 ways, B to C 4 ways⇒ A to C via B=6×4=24(ii) A to C via BC to A via BA _ B _ C _ B _ A 6 4 4 6No. of ways=6×4×4×6=24×24=576.

There are $6$ roads between $A$ and $B$ and $4$ roads between $B$ and $C$ .
(i) In how many ways can one drive from $A$ to $C$ by way of $B$ ?
(ii) In how many ways can one drive from $A$ to $C$ and back to $A$ , passing through $B$ on both trips?

$6$ roads between A and B
$4$ roads between B and C
(i) A to C via B
A to B $6$ ways, B to C $4$ ways
$\Rightarrow$ A to C via B $= 6 \times 4 = 24$
(ii) A to C via B
C to A via B
A _ B _ C _ B _ A
$6$ $4$ $4$ $6$
No. of ways $= 6 \times 4 \times 4 \times 6 = 24 \times 24 = 576$ .