3. There are seven students who always compare their CS test grades. They discovered that either the sum of two grades or the difference of two grades was always divisible by 10. Use the Pigeonhole Principle to show that for any seven positive integers, either the sum of two or the difference of two is divisible by 10.
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.
It is given that there are seven students who always compare their CS test grades. They discovered that either the sum of two grades or the difference of two grades was always divisible by 10.
Trending now
This is a popular solution!
Step by step
Solved in 4 steps with 2 images
