The streets of a city are arranged like the lines of a chess board. There are $5$ streets running North to South and $3$ streets running East to West. The number of ways in which a man can travel from NW to SE corner going the shortest possible distance is:

\frac{6!}{4! 2!}

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56

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\frac{8!}{5! 3!}

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15

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Solution

The correct options are
A $\frac{6!}{4! 2!}$
D $15$
Here we should go $(3 - 1)$ steps to east and $(5 - 1)$ steps to south.

So the total steps we should go $= 5 + 3 - 2$ ways

Hence the total number of ways $=^{5 + 3 - 2} C_{5 - 1} .^{3 - 1} C_{3 - 1}$
$=^{6} C_{4} .^{2} C_{2}$
$= \frac{6!}{4! 2!} (^{2} C_{2} = 1)$
$= \frac{6 \times 5 \times 4!}{4! 2!} = \frac{6 \times 5}{2} = 15$ ways.

Option $(a)$ and $(d)$ are correct.

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Q. The streets in a city are arranged like the lines of a chess-board. There are six streets running north and south, and five streets running along east-west. Find the number of ways in which a man can travel from the north-west to the south-east corner, going the shortest possible distance.

Question 2 (i)
(Street Plan) : A city has two main roads which cross each other at the centre of the city. These two roads are along the North-South direction and East-West direction.
All the other streets of the city run parallel to these roads and are 200 m apart. There are 5 streets in each direction. Using 1cm = 200 m, draw a model of the city on your notebook. Represent the roads/streets by single lines. There are many cross- streets in your model. A particular cross-street is made by two streets, one running in the North-South direction and another in the East-West direction. Each cross street is referred to in the following manner: If the 2nd street running in the North-South direction and 5th in the East-West direction meet at some crossing, then we will call this cross-street (2, 5). Using this convention, find:

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Q. (Street plan): A city has two main roads which cross each other at the center of the city. These two roads are along the North-South direction and East-West direction. All the other streets of the city-run parallel to these roads and are

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There are many cross-streets in your model. A particular cross-street is made by two streets, one running in the North-South direction and another in the East-West direction. Each cross street is referred to in the following manner: If the

2^{n d}

street running in the North-South direction and

5^{t h}

in the East-West direction meet at some crossing, then we will call this cross-street

(2, 5)

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(i)

How many cross-streets can be referred to as

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(i i)

How many cross-streets can be referred to as

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(Street Plan): A city has two main roads which cross each other at the centre of the city. These two roads are along the North-South direction and East-West direction.

All the other streets of the city run parallel to these roads and are 200 m apart. There are about 5 streets in each direction. Using 1 cm = 100 m, draw a model of the city on your notebook Represent the roads/streets by single lines.

There are many cross-streets in your model. A particular cross-street is made by two streets, one running in the North-South direction and another in the East-West direction. Each cross street is referred to in the following manner: If the 2^nd street running in the North-South direction and 5^th in the East-West direction meet at some crossing, then we will call this cross-street (2, 5). Using this convention, find:

(i) How many cross - streets can be referred to as (4, 3).

(ii) How many cross - streets can be referred to as (3, 4).

Q. A city has two main roads which cross each other at the centre of the city. These two roads are along the North-South direction and East-West direction. All other streets of the city run parallel to these roads and are 200 m apart. There are 5 streets in each direction.

Using 1 cm = 200 m, draw a model of the city on your notebook. Represent the roads/streets by single lines.

There are many cross-streets in your model. A particular cross-street is made by two streets, one running in the North-South direction and another in the East-West direction. Each cross street is referred to in the following manner: If the 2nd street running in the North-South direction and 5th in the East-West direction meet at some crossing, then we will call this cross-street (2,5). Using this convention, find:

(i) how many cross-streets can be referred to as (4,3).
(ii) how many cross-streets can be referred to as (3,4).

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The streets of a city are arranged like the lines of a chess board. There are 5 streets running North to South and 3 streets running East to West. The number of ways in which a man can travel from NW to SE corner going the shortest possible distance is:

The correct options are A 6!4!2! D 15Here we should go (3−1) steps to east and (5−1) steps to south.So the total steps we should go=5+3−2 waysHence the total number of ways = 5+3−2C5−1.3−1C3−1=6C4.2C2=6!4!2! (2C2=1)=6×5×4!4!2!=6×52=15 ways.Option (a) and (d) are correct.

The streets of a city are arranged like the lines of a chess board. There are $5$ streets running North to South and $3$ streets running East to West. The number of ways in which a man can travel from NW to SE corner going the shortest possible distance is: