Permutations and Combinations

The number of ways five alphabets can be chosen from the alphabets of the word MATHEMATICS, where the chosen alphabets are not necessarily distinct, is equal to:

1. 179
2. 177
3. 175
4. 181

The number of triangles whose vertices are at the vertices of a regular octagon but none of whose sides is a side of the octagon is

1. 56
2. 16
3. 24
4. 48

If all the words with or without meaning made using all the letters of the word "NAGPUR" are arranged as in a dictionary, then the word at 315th position in this arrangement is :

1. NRAPUG
2. NRAGUP
3. NRAPGU
4. NRAGPU

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

The number of ways of getting a sum 16 on throwing a dice four times is .

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

There are 4 men and 5 women in Group A, and 5 men and 4 women in Group B. If 4 persons are selected from each group, then the number of ways of selecting 4 men and 4 women is .

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