Arrangements when order matters: the formula for nPr, arrangements with repeated objects, and arrangements under conditions such as letters that must stay together.
3 lessons, about 1 h 15 min3 simulations11 problems3 practice questionsPython in every lesson
Created by StemPy LabA permutation is an arrangement of objects in a definite order. Filling places from different objects gives ways, written . With , the formula also gives . When repeats are allowed, every place has choices, so there are arrangements.
When some objects are alike, swapping two of them gives no new arrangement. So objects, with alike of one kind, alike of another and so on, have arrangements. Count all the orders as if every object were different, then divide out the orders of each group of equal objects.
Conditions change the count. To keep some objects together, glue them into one block and multiply by the orders inside it. To keep them apart, subtract the together count from the total. Fill restricted places first: the first digit of a number cannot be , and the last digit decides if it is even. The rank of a word counts the words before it in dictionary order.
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