1. The problem statement, all variables and given/known data Consider the word MATHEMATICS. There are some vowels: AEAI The remaining 7 letters are MTHMTCS. Find the number of different 11 lettered words formed from these particular letters (repetition not allowed) such that all the vowels occur in the same order AEAI. For example: SCAHTEAIMMT 3. The attempt at a solution The total number of words that can be formed is 11! without any restrictions. If we fix the A at place 1: no. of combinations of 3 from remaining: 10C3 If we fix the A at place 2: no. of combinations of 3 from remaining: 9C3 If we fix the A at place 3: no. of combinations of 3 from remaining: 8C3 ..... ..... Therefore the number of arrangements should be: 10C3+9C3+8C3+.........+3C3 =330 which gives me a wrong answer. Why? What should I do to get a correct answer?