+14 1. A teacher arranged her books on a shelf. She has 4 astronomy books, 3 Biology books, and 2 Chemistry books. How many ways can she arrange these books on the shelf if the books from each subject must be together?
2. How many ways can David, Sam, Emma, and Lanie stand in a line if David and Sam refuse to stand next to each other?
+128474 1. A teacher arranged her books on a shelf. She has 4 astronomy books, 3 Biology books, and 2 Chemistry books. How many ways can she arrange these books on the shelf if the books from each subject must be together?
The number of ways = arrangements in each topic * arrangements of topics = 4! * 3! * 2! * 3! =
1728 arrangements
2. How many ways can David, Sam, Emma, and Lanie stand in a line if David and Sam refuse to stand next to each other?
Number of ways without restrictions = 4! = 24
Number of ways if David and Sam DO stand next to each other = 3 places they can occupy * 2 arrangements in each place = 6
So.....number of ways if they refuse to stand next to each other = 24 - 6 = 18 ways
