My thought process goes like this -

Total number of balls = 10+8+5 = 23

Three balls are selected in 23 C 3 ways.

As first ball is black ball it can be selected in 10 C 1 ways and remaining 2 balls are selected in 8 C 2 ways.

Probability is 10.(8 C 2)/(23 C 3).

But the book answer is 4/33.

Anshu.