27. How many ways can the word MATHEMATICS be partitioned so that each part contains at least one vowel? For example, MA-THE-MATICS, MATHE-MATICS, MATHEM-A-TICS and MATHEMATICS are such partitions.
27. Ans: 36
To determine the number of partitions, we just have to decide the number of ways of inserting a partition between two consecutive vowels if we insert a partition at all. Thus the total number of partitions is $4 \times 3 \times 3=36$.