a. You can choose 4 marbles out of 9+7+5=21 by C_{4}^{21}=21!/(4!*(21-4)!)=21!/(4!*17!)=18*19*20*21/24=
=3*19*5*21=5985 ways. 2 white marbles can be chosen by C_{2}^{7}=21 ways, 2 blue marbles can be chosen by C_{2}^{5}=10 ways. Overall number of ways to choose 2 white and 2 blue marbles is 21*10=210.
Probability to choose 2 white and 2 blue marbles is:
P=210/5985=2/57≈0.0035=0.35%
b. The probability that marbles are not of the same color is 1-P(marbles are of the same color). Let us figure the probability that marbles are of the same color. It is the sum of probabilities that marbles are all blue, or white, or red.
P(marbles are all blue)=C_{4}^{5}/5985=5/5985=1/1197;
P(marbles are all white)=C_{4}^{7}/5985=35/5985=1/171;
P(marbles are all red)=C_{4}^{9}/5985=126/5985=2/95;
P(marbles are of the same color)=P(marbles are all blue)+P(marbles are all red)+P(marbles are all white)=(5+35+126)/5985=166/5985≈0.0277=2.77%
Probability that they are not of the same color is:
P=1-166/5985=5819/5985≈0.9723=97.23%
Comments
Comment