For an examination a candidate has to select 7 questions from three different groups $$\mathrm{A}, \mathrm{B}$$ and C. The three groups contain 4, 5 and 6 questions respectively. In how many different ways can a candidate make his selection if he has to select atleast 2 questions from each group?

The letters of the word "COCHIN" are permuted and all the permutations are arranged in alphabetical order as in an English dictionary. The number of words that appear before the word "COCHIN" is

The number of four digit numbers strictly greater than 4321 formed using the digits $$0,1,2,3,4,5$$ with repetition of digit is

A student has 3 library cards and 8 books of his interest in the library. Out of these 8 books he does not want to borrow Chemistry part 2 unless he can borrow Chemistry part 1 also. In how many ways can he choose the three books to be borrowed?