(b) There are 7 + 5 = 12 balls in the bag and the number of ways in which 4 balls can be drawn is 12C4 and the number of ways of drawing 4 black balls (out of seven) is 7C4.Hence, P (4 black balls)
7C4
12C4
=
7.6.5.4
1.2.3.4
×
1.2.3.4
12.11.10.9
=
7
99
Thus the odds against the event ‘all blackballs’ are (1−