Combinatorics and Mathematical Induction

Matching exercise

    
Match the items on the right to the items on the left.
Find the number of ways of arranging the letters of the word RAMANUJAN so that the relative positions of vowels and consonants are not changed.
How many numbers can be formed using the digits 1,2,3,4,2,1 such that, even digits occupies even place?
If the different permutations of all letters of the word BHASKARA are listed as in
a dictionary, how many strings are there in this list before the first word starting with B?
4 boys and 4 girls form a line with the boys and girls alternating. Find the number of ways of making this line.
240
9
2520
1152