A gentle reminder. “A permutation of a set of distinct objects is an ordered arrangement of these objects.” Theorem: “If n is a positive integer and r is an integer with 1 ≤ r ≤ n, then there are P (n, r ) = n(n − 1)(n − 2) · · · (n − r […]
How many permutations of the letters ABCDEFG contain Read More »
How to address this question? First, we need to see that we are asked: “in how many ways a set can be selected”. As per the definition of a set, we should know that the elements in a set don’t have an order. In other words, a set is an unordered collection of elements. So,
In how many ways can a set of five letters be selected from the English alphabet? Read More »
Let’s examine the first question. How many bit strings of length 10 contain exactly four 1s? From the question, you can see that the order of the four 1s does not matter. We just need to find out how many bit strings of length 10 contain exactly four 1s. This reminds me of a definition.
How many bit strings of length 10 contain: Read More »
Before starting to solve the exercise, let’s start with the definitions. “A permutation of a set of distinct objects is an ordered arrangement of these objects.” It is also important to know beforehand how many of these ordered arrangements are there. So, we don’t forget anyone when asked this type of question. Theorem: “If n
Like in other exercises, we should start with the definitions. “A permutation of a set of distinct objects is an ordered arrangement of these objects.” It is also important to know beforehand how many of these ordered arrangements are there, so we don’t forget anyone when asked this type of question. Theorem: “If n is
List all the permutations of {a, b, c} Read More »
