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Given, (x - 2)(x - 4)^{2}

=> (x - 2)(x - 4)^{2} = (x - 2)(x^{2} + 16 - 8x)

[Using identity, (a - b)^{2} = a^{2} + b^{2} - 2ab]

=> (x - 2)(x^{2} + 16 - 8x) = x(x^{2} + 16 - 8x) - 2(x^{2} + 16 - 8x)

= x^{3} + 16x - 8x^{2} - 2x^{2} - 32 + 16x

= x^{3 }- 10x^{2} + 32x - 32

=> (x - 2)(x - 4)^{2} = x^{3 }- 10x^{2} + 32x - 32

=> (x - 2)(x - 4)

[Using identity, (a - b)

=> (x - 2)(x

= x

= x

=> (x - 2)(x - 4)

Given

Perimeter of rectangle = 50

Let width of the rectangle = x

Then length of rectangle = 2x - 5

[Perimeter of rectangle = 2(Length + Breadth)]

=> 50 = 2(2x - 5 + x)

=> 50 = 2(3x - 5)

=> 50 = 6x - 10

=> 50 + 10 = 6x

=> 60 = 6x

=> x = 10

So length of rectangle = 2x - 5 = 2 * 10 - 5

= 20 - 5 = 15

=> Width of the rectangle = 10 inch

and length of rectangle = 15 inch

Perimeter of rectangle = 50

Let width of the rectangle = x

Then length of rectangle = 2x - 5

[Perimeter of rectangle = 2(Length + Breadth)]

=> 50 = 2(2x - 5 + x)

=> 50 = 2(3x - 5)

=> 50 = 6x - 10

=> 50 + 10 = 6x

=> 60 = 6x

=> x = 10

So length of rectangle = 2x - 5 = 2 * 10 - 5

= 20 - 5 = 15

=> Width of the rectangle = 10 inch

and length of rectangle = 15 inch

Sample Space = {(1, 1), (1, 2), .......(1, 6), (2, 1), (2, 2),......,(2,
6), (3, 1), (3, 2),.........., (3, 6), (4, 1), (4, 2), ..............,
(4, 6), (5, 1), (5, 2), ......, (5, 6), (6, 1), (6, 2), .........., (6,
6)}

Total number of possible outcomes = 36

Possible outcomes getting sum of 2 = {(1,1)}

Number of favorable outcomes = 1

P(getting sum of 2) = $\frac{Number of Favorable Outcomes}{Number of Possible Outcomes}$

= $\frac{1}{36}$

=> P(getting sum of 2) = $\frac{1}{36}$.

Total number of possible outcomes = 36

Possible outcomes getting sum of 2 = {(1,1)}

Number of favorable outcomes = 1

P(getting sum of 2) = $\frac{Number of Favorable Outcomes}{Number of Possible Outcomes}$

= $\frac{1}{36}$

=> P(getting sum of 2) = $\frac{1}{36}$.