Permutations and Combinations

In an examination of Mathematics paper, there are 20 questions of equal marks and the question paper is divided into three sections : A, B and C. A student is required to attempt total 15 questions taking at least 4 questions from each section. If section A has 8 questions, section B has 6 questions and section C has 6 questions, then the total number of ways a student can select 15 questions is .

All the letters of the word "GTWENTY" are written in all possible ways with or without meaning and these words are written as in a dictionary. The serial number of the word "GTWENTY" is .

Number of ways of arranging 8 identical books into 4 identical shelves where any number of shelves may remain empty is equal to

1. 18
2. 16
3. 12
4. 15

n-1Cr= (k2-8 )nCr+1 if and only if :

1. 2 2<k<2 3
2. 2 2<k 3
3. 2 3<k<3 3
4. 2 3<k 3 2

Let = (4!)!(4!)3! and = (5!)!(5!)4!. Then :

1. and
2. and
3. and
4. and