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Two distinct integers x and y are chosen, without replacement, at random from the set `{ x , y | 0 le x le 10 , 0 le y le 10` , x and y are in integers} the probability that `|x - y| le 5` is :

A

`(87)/(121)`

B

`(88)/(121)`

C

`(91)/(121)`

D

`(101)/(121)`

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The correct Answer is:
B
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x - y le 2

Two integers x and y are chosen with replacement out of the set {0, 1, 2, . . . 10}. The probability that |x - y| doesn't exceed 5 is

x-y le 2, x + y le 4 , x ge 0, y ge 0

y - 2x le 1, x + y le 2, x ge 0, y ge 0

x + 2y le 40, 2x + y le 40, x ge 0, y ge 0

x + y le 10, 4x + 3y le 24,x ge 0, y ge 0

x + y le 6, x + y ge 4

x + 2y le 10, x + y ge 1, x-y le 0, x ge 0, yge 0

2x + y le 6, x + 2y le 8, x ge 0, y ge 0

Find the area of region : {(x,y) : 0 le y le x^(2) + 1, 0 le y le x + 1,0 le x le 2} .

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