Keep the meeting and lunch seating models separate

(a) Find the number of ways the letters of POSITIVE can be arranged if

(i) all vowels must be next to each other,2 marks

(ii) the vowels are separated and the arrangement begins and ends with I.2 marks

(b) The Mathematics Department of M Institute consists of 11 teachers, including Mr Tan and Mr Lin. At a meeting, all 11 teachers sit at a round table with numbered seats. How many arrangements have Mr Tan and Mr Lin next to each other?3 marks

After the meeting they find a circular table for 6 and a long table with a row of 5 seats at a food court, as shown. Find the number of arrangements of all 11 teachers at these two tables such that Mr Tan is seated next to Mr Lin.4 marks