What are your chances of winning the following lottery? You choose a set of 10 distinct numbers from the set S={1,…,50}, and the person running the lottery selects 6 (distinct) numbers at random, also from the set S. If all six selected numbers are a subset of your chosen set of 10 numbers, then you win.
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.
What are your chances of winning the following lottery? You choose a set of 10 distinct numbers from the set S={1,…,50}, and the person running the lottery selects 6 (distinct) numbers at random, also from the set S. If all six selected numbers are a subset of your chosen set of 10 numbers, then you win.
Step by step
Solved in 2 steps with 1 images
