a) Consider the letters of the word INDEPENDENCE. Find the number of arrangements for the following conditions: i . The letters start with P. (1 mark) ii. The vowels always come together. (2 marks) ili. The word begins with I and end with P. (2 marks) b) How many numbers lying between 100 and 1000 can be formed with the digits 0. 1. 2. 3. 4 and 5 if the repetition of the digits is not allowed? (2 marks) c) A delegation of four students is selected each year from a college to attend the meeting of Mathematics Student Association. There are twelve eligible students to be chosen. How many ways: i. the delegation can be chosen? (1 mark) ii. if two of the eligible students will not attend the meeting together