This document provides examples of permutation problems with conditions. It asks the reader to calculate the number of possible arrangements of people or objects in different scenarios where certain restrictions apply, such as groups staying together or letters being arranged in a specific order. The examples include arranging couples in a row where couples may or may not stay together, arranging books on a shelf with or without restrictions on subject grouping, arranging students in a row where some insist on staying together, arranging people around a table with gender-based grouping, and arranging the letters in the word "ONLINE" under different restrictions.

1. Permutation with
Condition
Mathematics10

2. Examples
1. Five couples want to have their picture taken. In how many can they arrange
themselves in a row if:
a. If they may stand anywhere?
b. Couples may stay together?
2.There are 4 different Mathematics books and 5 different Science books. In how
many ways can the books be arranged on a shelf if.
a. There are no restrictions
b. Books on the same subject must be placed together?

3. Activity # 6.
1.In how many ways can a group of 8 students stand in a row if three of them
insist to stay together?
2. In how many ways can 3 women and 4 men sit in a round table if the women
always sit together?
3.How many ways can the letters in the word ONLINE be arranged if
a. There are no restriction?
b. The letter E and O are together?
c. All consonants are together?
d. All vowels are together