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  4. 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

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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

Permutations and Combinations

Solution:

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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 $\frac{8!}{4!4!} = 70$