3. 2 white, 6 red and 4 green balls. 4 balls are selected at random what is the sample space are. (a) 495 (b) 11880 (c) 48 (d) 16
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6 Red, 5 Black , 4 White
Total 15 balls out of which 4 balls to be drawn.
Total combinations= 15c4 = 1365 ways
There will be 3 possibilities.
Two red balls, 1 black , 1 white
2 Red….. 6c2 =15, 1black……. 5c1= 5, 1 white………. 4c1=4
Total= 15*5*4 =300
Two black balls, 1 red , 1 white
2 Black….. 5c2 =10, 1 red……. 6c1= 6, 1 white………. 4c1=4
Total= 10*6*4= 240
Two white balls, 1 red, 1 black
2 White….. 4c2 =6, 1 black……. 5c1= 5, 1 red………. 6c1=6
Total= 6*5*4 =180
So the required probability is
(300+240+180)/1365 = 720/1365
48/91
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