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If x lt 4 " and " x, y in {1, 2, 3, .., ...

If `x lt 4 " and " x, y in {1, 2, 3, .., 10}`, then find the number of ordered pairs (x,y).

Text Solution

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We have `x lt 4 lt y`, where `x, y in {1,2,3,..,10}`
`therefore ` x can be 1,2 or 3 and y can be 5,6,7,8,9, 10.
Thus, for x we have 3 options and for y we have 6 options.
So, using multiplication rule of counting, Number of ordered paris `=3xx6=18`
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