Probability of picking 4 red balls 
There are $6$ red balls and $5$ blue balls in a jar. You pick any $4$ balls without looking in  the jar. What is the probability that you would be having $4$ red balls in hand?

Note that you're picking up all the $4$ balls in one single attempt and not one-by-one. Also balls of same colour are to be considered as identical. 
I tried this and got the answer as $4/11$ which was wrong. I can't figure out what the cases (sample space) would be.
 A: Well its very simple.
See first lets calculate the sample space. It would be 
$$
{^{11}C_4} 
$$
because you are choosing a total of 4 balls out of 11 balls.
Next  you need to calculate the favorable event
so you have 6 blue balls and favorable would be when you take out 4 blue ones. 
which can be done by
$$
{^6C_4} 
$$
ways. So the probability becomes
$$
={{^6C_4}\over{^{11}C_4}} \\={1\over 22}
$$
If you dont get it by this method here is the basic step by step trick:-
Probability of getting first blue ball is
$$
={6\over 11}
$$
as there are total 11 and 6 blue
now Probability of getting Second blue ball is
$$
={5\over 10}
$$
because you took out 1 ball from total which is blue so both numbers reduce by 1.
similarly
3rd blue ball
$$
={4\over 9}
$$
and 4th one
$$
={3\over 8}
$$
so final probablity is
$$
P =\frac{6}{11} \cdot \frac{5}{10}\cdot \frac{4}{9}\cdot \frac{3}{8}\\P=\frac{360}{7920}\\P=\frac{1}{22}\\
$$
A: You are picking 4 balls without replacement. The probability that you pick four red balls is $$P =\frac{6}{11} \cdot \frac{5}{10}\cdot \frac{4}{9}\cdot \frac{3}{8}\\P=\frac{360}{7920}\\P=\frac{1}{22}\\P \approx 0.045 \\P \approx 4.5\%$$
A: Since you have to pick 4 balls, the number of elements in the sample space would be $^{11}C_4$ ("11 choose 4"). The number of ways of picking all red balls would be $^6C_4$. 
Therefore, the probability would be $$={{^6C_4}\over{^{11}C_4}} \\ ={1\over 22}$$
A: The answer is easly given considering permutations. Indeed the probability is:
$$P =\frac{7!}{11!} \cdot \frac{6!}{2!}=\frac{1}{22}$$
where


*

*$11$ is the total number of balls;

*$7$ the number of balls remaining in the jar;

*$6$ the number of red balls;

*$2$ the number of red balls remaining in the jar.

