A box contain 2 red , 1 blue and 2 green identical balls. Three balls are drawn at random in succession without replacement. Write the sample space.

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Suman Ghosh

SME in Mathematics & Statistics

The sample space is {RRB, RBR, BRR, GGB, GBG, BBG, RRG, RGR, GRR, GGR, GRG, RGG, RBG, RGB, BRG, BGR, GRB, GBR} Here R = Red ball, G = Green ball, B = Blue ball
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R: Red B:Blue G: Green Sample Space = { RRB , RBR , BRR, GGB , GBG , BBG , RRG , RGR , GRR , GGR , GRG, RGG , RBG , RGB , BRG , BGR , GRB , GBR }
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(RRB, RRG, BGG, GGR, GBR)
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S = {RRB, RRG, RBR, RBG, RGR, RGB, RGG, GGB, GGR, GBG, GBR, GRG, GRB, GRR, BGG, BRR, BRG, BGR} Total choices = 5C3 = 10. Out of this red ball 1 and red ball two are indistinguishable. Similarly green ball 1 and green ball 2 are indistinguishable. So total of four possibilities are...
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S = {RRB, RRG, RBR, RBG, RGR, RGB, RGG, GGB, GGR, GBG, GBR, GRG, GRB, GRR, BGG, BRR, BRG, BGR} Total choices = 5C3 = 10. Out of this red ball 1 and red ball two are indistinguishable. Similarly green ball 1 and green ball 2 are indistinguishable. So total of four possibilities are removed [2*2!]. We are left with 6 possibilities. As sequence is important...there are 3 places. 3*6= total 18 possibilities. read less
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Math Educator for Std.11th ,12th , Engineering Entrance and Degree Level with 11+ Years Experience

Write the sample space Chandana and not the number of sample space..
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Math Educator for Std.11th ,12th , Engineering Entrance and Degree Level with 11+ Years Experience

WRITE THE SAMPLE SPACE Mam Moushumi.. your concept and answer totally wrong.
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Teacher

For the First ball sample space is 5,for the second ball the sample space 4,for the third ball the sample space is 3.
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Math analyst

Sample space is set of all possible outcomes. if R,G,B corresponds to red green blue balls sample space = { (R,R,B),(R,B,R),(B,R,R), (G,G,B),(G,B,G),(B,G,G), (R,R,G),(R,G,R),(G,R,R), (G,G,R),(G,R,G),(R,G,G), (R,G,B),(R,B,G),(G,B,R) }.
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Mathematics Expert

Sample space is the all possible outcome!!!!
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