The total number of integral solutions of the equation x- y-z-w - 20 where x - 1- y - 2- z - 3- w - 4 is 143k- Then the value of k is

Let x =X+1, y=Y + 2, z = Z + 3,w = W +4 Then, X+Y+Z + W = 10 where X,Y,Z,W≥ 0 Number of integral solutions =^10+4 1C_4 1 = ^13C_3=286. nbsp; (using beggar's ...

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The total number of integral solutions of the equation $x + y + z + w = 20$ where $x \geq 1, y \geq 2, z \geq 3, w \geq 4$ is $143 k .$ Then the value of $k$ is

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Let $x = X + 1, y = Y + 2, z = Z + 3, w = W + 4$
Then, $X + Y + Z + W = 10$ where $X, Y, Z, W \geq 0$

Number of integral solutions
$=^{10 + 4 - 1} C_{4 - 1} =^{13} C_{3} = 286.$ (using beggar's method)
Now, $143 \times 2 = 143 k$
$\Rightarrow k = 2$

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The total number of integral solutions of the equation x+y+z+w=20 where x≥1,y≥2,z≥3,w≥4 is 143k. Then the value of k is

Let x=X+1,y=Y+2,z=Z+3,w=W+4 Then, X+Y+Z+W=10 where X,Y,Z,W≥0 Number of integral solutions =10+4−1C4−1=13C3=286. (using beggar's method) Now, 143×2=143k ⇒k=2

The total number of integral solutions of the equation $x + y + z + w = 20$ where $x \geq 1, y \geq 2, z \geq 3, w \geq 4$ is $143 k .$ Then the value of $k$ is

Let $x = X + 1, y = Y + 2, z = Z + 3, w = W + 4$
Then, $X + Y + Z + W = 10$ where $X, Y, Z, W \geq 0$

Number of integral solutions
$=^{10 + 4 - 1} C_{4 - 1} =^{13} C_{3} = 286.$ (using beggar's method)
Now, $143 \times 2 = 143 k$
$\Rightarrow k = 2$