A bag contains 30 tickets numbered 1,2,3, ….30 of which 5 tickets are drawn at random
and  arranged in ascending order. Find the probability that the third number is 20.

Dear student,

Ways os selecting 5 out of 30 is C530let the tickets be 20, a,b,c,dArranging them in ascending order : a, b, 20, c, da,b has to lie within 1 to 19=C219c,d  has to lie within 21 to 30= C210so, C219×C210C530=19×18×17!2!×17!×10×9×8!2!×8!30×29×28×27×26×25!5!×25!=19×9×5×9×5×4×3×2×130×29×28×27×26on solving we get2855278

Regards

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