OPTION A) 12C2
OPTION B) 10C2
OPTION C) 12C3
OPTION D) 10C3
Ways to Select 10 Balls
To find the total number of ways of selecting 10 balls out of an unlimited number of identical white, red, and blue balls, we can use a technique called stars and bars.
In this case, we can represent the selection of balls using stars and bars as follows:
Let x1 represent the number of white balls selected.
Let x2 represent the number of red balls selected.
Let x3 represent the number of blue balls selected.
We need to find the number of non-negative integer solutions to the equation x1 + x2 + x3 = 10, where x1, x2, and x3 are non-negative integers.
Using the stars and bars formula, the total number of ways is given by:
C(n+k-1, k-1)
where n is the total number of objects (10 in this case) and k is the number of categories (3 in this case).
Plugging in the values, we have:
C(10+3-1, 3-1) = C(12, 2)
Using the formula for combinations, we have:
C(12, 2) = 12! / (2! * (12-2)!) = 12! / (2! * 10!)
Simplifying further:
12! = 12 * 11 * 10!
Cancelling out the 10! terms:
C(12, 2) = (12 * 11) / (2 * 1) = 66
Therefore, the total number of ways of selecting 10 balls out of an unlimited number of identical white, red, and blue balls is 66.
