Shortcut:
A box contains 'p' red balls, 'q' black balls. If two draws of three balls each are made, the ball being replaced after the first draw, then the chance that the balls were red in the first draw and black in the second draw is given by
^{p}C_{3} x ^{q}C_{3}
/
^{((p + q)C3 )2}
Here, p = 5, q = 8
Using these values in the shortcut, we get:
Required Probability =
^{5}C_{3} x ^{8}C_{3}
/
^{((5 + 8)C3 )2}
=
(5 x 4 x 3) x (8 x 7 x 6)
/
(13 x 12 x 11)^{2}
=
5 x 4 x 3 x 8 x 7 x 6
/
13 x 12 x 11 x 13 x 12 x 11
=
5 x 4 x 7
/
13 x 11 x 13 x 11
=
140
/
20449
