1). How many distinct arrangements can be made using the letters of the word "MATHEMATICS" such that no two adjacent letters are the same?
2). In how many ways can you arrange the digits 1, 2, 3, 4, 5, 6, 7, 8, 9 such that no even digit appears at an even-numbered position?
3). How many different ways can you arrange the letters in the word "STATISTICS" such that no two T's are adjacent?
4). If there are 10 books on a shelf, including 3 math books, 2 science books, and 5 literature books, how many ways can they be arranged such that all the books of the same subject are grouped together?
5). A lock consists of 4 digits. How many different combinations are possible if the digits must be distinct, and the first digit is odd, and the last digit is even?
6). How many distinct 4-digit numbers can be formed using the digits 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9 if no digit can be repeated, and the number must be divisible by 4?
7). A team of 5 basketball players is selected from a group of 10 players, including 3 forwards and 7 guards. How many different teams can be formed with 2 forwards and 3 guards?
8). How many distinct arrangements can be made using the letters of the word "PROBABILITY"?
9). If you have 5 red balls, 4 blue balls, and 3 green balls, how many different ways can you arrange them in a line such that no two adjacent balls have the same color?
10). How many different permutations can be formed using the digits 1, 2, 3, 4, 5, 6, 7, 8, and 9 such that the odd digits are all together and the even digits are all together?
11). Calculate the number of distinct arrangements of the letters in the word "EQUATION" such that no two vowels are adjacent.
12). How many different ways can you arrange the letters in the word "SYMMETRY" such that no two Y's are together?
13). If you have 6 different books by different authors and you want to arrange them on a shelf such that no two books by the same author are adjacent, how many different arrangements are possible?
14). A box contains 4 red balls, 3 green balls, and 2 blue balls. How many different ways can you arrange these balls in a row such that no two balls of the same color are adjacent?
15). How many different ways can 8 students sit in a row such that 2 specific students refuse to sit next to each other?
16). Calculate the number of distinct permutations of the word "REFLECTION" such that no two vowels are adjacent.
17). In how many ways can you arrange the letters in the word "MAGNIFICENT" such that no two consonants are adjacent?
18). How many different ways can you arrange the letters in the word "COMPLEXITY" such that no two X's are adjacent?
19). Calculate the number of distinct permutations of the word "UNIVERSITY" such that no two vowels are adjacent.
20). How many different ways can you arrange the digits 1, 2, 3, 4, 5, 6, 7, 8, 9, and 0 such that no two odd digits are adjacent?
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