(a)[3]
Determine the number of distinct ways the $13$ letters of ACCOMMODATION can be arranged in a straight line if the vowels $(A, I, O)$ are all adjacent.
(b)[5]
At an international conference there are $7$ Chinese students, $6$ European students and $4$ American students. Four students are to be selected to take part in a television broadcast. Find the number of different ways the students may be chosen if the selection includes at least one Chinese student and at least one European student.