Question

A bag contains a large number of red, green, and blue balls. Ten balls are randomly drawn from the bag, without regard to order. How many different color combinations can be drawn from the bag?

Example: one combination is 1 red, 3 green, and 6 blue balls.

Answer 1

here let x1,x2 and x3 are number of balls of three colors

therefore x1+x2+x3 =10

number of solution of above equation =(_10+3-1C_3-1) =(₁₂C₂) =12!/(2!*10!) =66