11. In the Colorado Power Ball Lottery you choose 5 white numbered balls from a group of 75 and 1 red ball from a group of 15. How many possible winning combinations are there? How many winning combinations contain the white number 2 and 8?
Permutations and Combinations
If there are 5 dishes, they can be relished in any order at a time. In permutation, it should be in a particular order. In combination, the order does not matter. Take 3 letters a, b, and c. The possible ways of pairing any two letters are ab, bc, ac, ba, cb and ca. It is in a particular order. So, this can be called the permutation of a, b, and c. But if the order does not matter then ab is the same as ba. Similarly, bc is the same as cb and ac is the same as ca. Here the list has ab, bc, and ac alone. This can be called the combination of a, b, and c.
Counting Theory
The fundamental counting principle is a rule that is used to count the total number of possible outcomes in a given situation.
In the colorado power ball Lottery you use a 5 white numbered balls from a group of 75 and 1 red ball from a group of 15 ball .
Use combination .
Combination : The number of ways to choose a sample of r elements from a set of n distinct objects where order does not matter and replacements are not allowed. It's formula is given as ,
Here , n = total number of balls & r is selected balls from group .
Total number of balls = 75 white ball + 15 red balls = 90 balls
Winning combinations = C(75,5) x C(15,1)
Therefore , Total winning combinations = 172593930 x 15 = 2,58,89,08,950
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