A particle from origin in a Cartesian co-ordinate plane is to be carried to point (4,4) such that the movement of the point at a line is either along x-axis or along y-axis. One of such way is (0,1), (1,1), (1,2), (1, 3), (2, 3), (3, 3), (4, 3), (4,4). The total number of such ways is

Question

A particle from origin in a Cartesian co-ordinate plane is to be carried to point (4,4) such that the movement of the point at a line is either along x-axis or along y-axis. One of such way is (0,1), (1,1), (1,2), (1, 3), (2, 3), (3, 3), (4, 3), (4,4). The total number of such ways is (A) 70 (B) 8! (C)  2 × 8! (D) None of these

Tardigrade Admin · Accepted Answer

<img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/mathematics/efe0a05aed6cbd71aacb0d46aea1d8d0-.png" /> We have to take the particle to 4 units along positive x - axis and 4 units along positive y - axis. In any two different ways of doing so the order of movement along x - axis and along y-axis do not change. Hence, total number of ways of doing so is (8!/4!4!) = 70

$70$

$8!$

$2 \times 8!$

None of these

We have to take the particle to $4$ units along positive $x$ - axis and $4$ units along positive $y$ - axis. In any two different ways of doing so the order of movement along $x$ - axis and along y-axis do not change. Hence, total number of ways of doing so is $\frac{8 !}{4 ! 4 !} = 70$

Q. A particle from origin in a Cartesian co-ordinate plane is to be carried to point (4,4) such that the movement of the point at a line is either along x-axis or along y-axis. One of such way is (0,1),(1,1),(1,2),(1,3),(2,3),(3,3),(4,3),(4,4). The total number of such ways is

70

8!

2×8!

None of these

We have to take the particle to 4 units along positive x - axis and 4 units along positive y - axis. In any two different ways of doing so the order of movement along x - axis and along y-axis do not change. Hence, total number of ways of doing so is 4!4!8!​=70

$70$

$8!$

$2 \times 8!$

We have to take the particle to $4$ units along positive $x$ - axis and $4$ units along positive $y$ - axis. In any two different ways of doing so the order of movement along $x$ - axis and along y-axis do not change. Hence, total number of ways of doing so is $\frac{8 !}{4 ! 4 !} = 70$