A box `B_(1)` contains 1 white ball, 3 red balls, and 2 black balls. An- other box `B_(2)` contains 2 white balls, 3 red balls and 4 black balls. A third box `B_(3)` contains 3 white balls, 4 red balls, and 5 black balls.
If 1 ball is drawn from each of the boxes `B_(1),B_(2) and B_(3),` the probability that all 3 drawn balls are of the same color is

Options

A. `82//648`
B. `90//648`
C. `558//648`
D. `566//648`

Answer

A

Explanation

P (required)
= P (all are white) + P (all are red) + P (all are black)
`=1/6xx2/9xx3/12+3/6xx3/9xx4/12+2/6xx4/9xx2/12=6/648+36/648+40/648=82/648`