Permutations and Combinations

The number of ways in which 21 identical apples can be distributed among three children such that each child gets at least 2 apples, is

1. 130
2. 136
3. 142
4. 406

If for some m, n; 6Cm+2 (6Cm+1 )+6Cm+2>8C3 and n-1P3:nP4=1:8, then nPm+1+n+1Cm is equal to

1. 380
2. 376
3. 372
4. 384

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