Question 267894
A box contains 8 blue marbles, 4 red marbles, 3 green marbles. 
Total number of balls = 8+4+3 = 15
A. if three marbles are selected at random,what is probability that all three marbles will be blue marbles

Total number of ways = 15C3 = (15*14*13) / (1*2*3) = 455
Out of 5 blue balls 3 can be selected in 5C3 ways.
The number of favourable ways = 5C3 = (5*4*3)/(1*2*3)=10
The probability that all three marbles will be blue marbles = 10/455 = 2/91

B. if three marbles are selected at random,what is probability that one of each colour be selected .

Total number of ways = 15C3 = (15*14*13) / (1*2*3) = 455
Out of 8 blue balls 1 can be selected in 8 ways,Out of 4 red balls 1 can be selected in 4 ways,Out of 3 green balls 1 can be selected in 3 ways, 
The number of favourable ways = 5C3 = (8*4*3)=96
The probability that all three marbles will be blue marbles = 96/455 

C. if 11 marbles are selected at random, what is the probability that no red marbles will be selected
Total number of ways = 15C11 = 15C4 = (15*14*13*12)/(1*2*3*4) = 1365
Leaving the 4 red balls there are 8 blue and 3 green balls.
So Out of 11 (blue balls+green ) 11 can be selected in 1 way.
The number of favourable ways = 1
The probability that all 11 marbles will be blue marbles or green = 1/455

D. if six marbles are selected at random, what is the probability that two of each color marble will be selected?
 
Total number of ways = 15C6 = (15*14*13*12*11*10)/(1*2*3*4*5*6) = 5005
Out of 8 blue balls 2 can be selected in 8C2 ways,Out of 4 red balls 2 can be selected in 4C2 ways,Out of 3 green balls 2 can be selected in 3C2 ways, 
The number of favourable ways = (8C2)*(4C2)*(3C2)=504 
The probability that that two of each color marble will be selected
= 504/5005