In trying to solve this problem, let's see if we can come up with some kind of a general formula for the number of distinguishable permutations of n objects when there are more than two different types of …

Find the number of ways of placing 12 balls in a row given that 5 are red, 3 are green and 4 are yellow. Another way to think about this problem is to choose five of the twelve spaces in which to place the …

For a set of n objects of which n1 are alike and one of a kind, n2 are alike and one of a kind, ... , nk are alike and one of a kind, the number of distinguishable permutations is:

Aug 1, 2025 · Find the number of ways of getting an ordered subset of r elements from a set of n elements as nPr (or nPk). Permutations calculator and permutations formula. Free online …

Sep 28, 2022 · 1 Your first part where you are talking of "indistinguishable" objects, the objects are not really indistinguishable, as they are divided into distinguishable types. In fact, both the (identical) …

How many ways are there to permute the letters in PYTHON if the P and Y cannot be adjacent? The approach here is to note that there are P(6; 6) ways to permute all of the letters and then count and …

The formula to calculate distinguishable permutations is: P = n! / (n1! * n2! * ... * nk!) Here, n is the total number of items to arrange, and n1, n2, …, nk is the factorial of each group’s identical items. In the …

Nov 28, 2025 · Distinguishable permutations count unique arrangements when items in a set are identical. The formula $N! / (n_1! \cdot n_2! \cdot \ldots \cdot n_k!)$ is used for calculation.

Jul 17, 2015 · Number of distinguishable permutations: If n objects are partitioned so that there are n1 of one kind, n2 of another, and n 3 of still a third kind (so that n1 + n2 + n3 =n), then the number of …

Dec 1, 2023 · In order to exclude the number of permutations that are effectively the same due to identical members, we need to divide the number of possible permutations of all the items by the …