Probability (Class 12)

A bookshelf contains 6 distinct books of Mathematics and 5 distinct books of Physics. From these 11 books, 6 books are chosen at random. Let X be the absolute value of the difference between the number of Mathematics books chosen and the number of Physics books chosen. If is the mean of the random variable X, then the value of 77 is .

Let X be a random variable, and let P(X=x) denote the probability that X takes the value x. Suppose that the points (x,P(X=x) ), x=0,1,2,3,4, lie on a fixed straight line in the xy-plane, and P(X=x)=0 for all x R-\0,1,2,3,4\. If the mean of X is 52, and the variance of X is , then the value of 24 is .