Permutations and Combinations

Let 0 r n. If n+1Cr+1 : nCr : n-1Cr-1 = 55 : 35 : 21, then 2n + 5r is equal to :

1. 62
2. 60
3. 55
4. 50

Let the set S = \2, 4, 8, 16, , 512\ be partitioned into 3 sets A, B, C with equal number of elements such that A B C = S and A B = B C = A C = . The maximum number of such possible partitions of S is equal to:

1. 1640
2. 1520
3. 1710
4. 1680

60 words can be made using all the letters of the word BHBJO, with or without meaning. If these words are written as in a dictionary, then the 50th word is:

1. OBBJH
2. HBBJO
3. OBBHJ
4. JBBOH

There are 5 points P1, P2, P3, P4, P5 on the side AB, excluding A and B, of a triangle ABC. Similarly there are 6 points P6, P7, , P11 on the side BC and 7 points P12, P13, , P18 on the side CA of the triangle. The number of triangles, that can be formed using the points P1, P2, , P18 as vertices, is:

1. 751
2. 776
3. 796
4. 771

If n is the number of ways five different employees can sit into four indistinguishable offices where any office may have any number of persons including zero, then n is equal to :

1. 47
2. 53
3. 51
4. 43

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

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