Permutations and Combinations

The number of elements in the set S=\(x, y, z): x, y, z , x+2y+3z=42, x, y, z 0\ equals .

The lines L1, L2, ,L20 are distinct. For n=1,2,3, ,10 all the lines L2n-1 are parallel to each other and all the lines L2n pass through a given point P. The maximum number of points of intersection of pairs of lines from the set \L1, L2, ,L20\ is equal to .

The total number of words (with or without meaning) that can be formed out of the letters of the word 'DISTRIBUTION' taken four at a time, is equal to .

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