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Question

Number of ways to choose an order pair (a,b) of numbers from the set {1,2,3..........10} such that |a-b|≤5 is



Your Answer
A

70

Your Answer
B

100

Correct Answer
C

80

Your Answer
D

90


Solution

The correct option is C

80


|ab|5 means| a-b|=0 or 1|ab|5|ab|=0a=b which is possible in 10 ways. Let x, y, z represent, numbers before, in between and after a and b then x+y+z=8,0y4 and x,z0

= coefficient of x8in(1+x+....x8)2(1+x+.....x4)

= 35

 a, b, can be in any order

 Total ways = 2×35+10=80.

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