A basket contains equal number of red balls and yellow balls. The objective is to pick out N balls in a random Eashion. The total number of balls in the basket is much greater than N. The number of ways of picking out ' n ' red balis and (Nn) yellow balls is given by =n!(Nn)!N! It is easy to show that is a maximum ( mxx ) when n=N/2. Assume that N is a sufficiently large number. Suppose now that we consider the number of ways of picking out (N/2+) red balls and (N/2E) yellow balls such that (2N+)(2N)N!when1sax, and yet InfotalInmax. Make calculations for N=1000. Hint: Replace the summation istal=j by an integral with b as a variable. That is, iotalN/2N/2()d A basket contains equal number of red balls and yellow balls. The objective is to pick out N balls in a random Eashion. The total number of balls in the basket is much greater than N. The number of ways of picking out ' n ' red balis and (Nn) yellow balls is given by =n!(Nn)!N! It is easy to show that is a maximum ( mxx ) when n=N/2. Assume that N is a sufficiently large number. Suppose now that we consider the number of ways of picking out (N/2+) red balls and (N/2E) yellow balls such that (2N+)(2N)N!when1sax, and yet InfotalInmax. Make calculations for N=1000. Hint: Replace the summation istal=j by an integral with b as a variable. That is, iotalN/2N/2()d<><>