[nilesh]

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I want the sample Permutation & Combination questions for preparation of IBPS Probationary Officers PO Exam?

[prince karak]

I am providing you the sample Permutation & Combination questions for IBPS Probationary Officers PO Exam.

IBPS PO Exam Permutation & Combination questions

How many positive numbers can be formed by using any number of the digits 0, 1, 2, 3 and 4, no digit being repeated in any number?
(a) 360
(b) 260
(c) 620
(d) 280
(e) None of these

In how many ways 3 prizes can be given away to 7 boys when each boy is eligible for any of the prizes?
(a) 243
(b) 343
(c) 433
(d) 2187
(e) None of these

How many words can be formed with the letters of the word “Pataliputra’ without changing the relative order of the vowels and consonants?
(a) 3600
(b) 6300
(c) 3900
(d) 4600
(e) None of these

How many different letter arrangements can be made from the letters of the word RECOVER?
(a) 1210
(b) 5040
(c) 1260
(d) 1200
(e) None of these

In how many different ways can the letters of the word JUDGE be arranged so that the vowels always come together?
(a) 48
(b) 24
(c) 120
(d) 60
(e) None of these

4 boys and 2 girls are to be seated in a row in such a way that two girls are always together. In how many different ways can they be seated?
(a) 120
(b) 720
(c) 148
(d) 240
(e) None of these

8 men entered a lounge simultaneously. If each person shook hands with the other then find the total no. of handshakes.
(a) 16
(b) 36
(c) 56
(d) 28
(e) None of these

In a party every person shakes hands with every other persons. If there was a total of 120 handshakes in the party, find the no. of persons who were present in the party.
(a) 15
(b) 18
(c) 16
(d) 20
(e) None of these

There are 8 members in a delegation which is to be sent abroad. The total no. of members is 18. In how many ways can the selection be made so that 2 members are always included?
(a) 8800
(b) 8008
(c) 8018
(d) 8080
(e) None of these

From 5 officers and 7 jawans in how many ways can 4 be chosen to include exactly 2 officer?
(a) 210
(b) 120
(c) 200
(d) 105
(e) None of these

From 8 officers and 12 jawans in how many ways can 7 be chosen to include exactly 3 officers?
(a) 27720
(b) 27270
(c) 26620
(d) 27660
(e) None of these

From a group of 6 men and 4 women a committee of 4 persons is to be formed.
(i) In how many different ways can it be done so that the committee has at least one woman?
(a) 210
(b) 225
(c) 195
(d) 185
(e) None of these

From 4 officers and 8 jawans in how many ways can be 6 chosen to include at least one officer?
(a) 896
(b) 986
(c) 886
(d) 996
(e) None of these

In how many ways 3 boys and 3 girls can be seated in a row so that boys and girls are alternate?
(a) 9
(b) 36
(c) 72
(d) Data inadequate
(e) None of these

Question

In how many different ways can the letters of the word "CHARGES" be arranged in such a way that the vowels always come together?

a) 1440 b) 720 c) 360 d) 240

Answer : a) 1440

Solution :

The arrangement is made in such a way that the vowels always come together.
i.e., "CHRGS(AE)".

Considering vowels as one letter, 6 different letters can be arranged in 6! ways; i.e., 6! = 720 ways.

The vowels "AE" can be arranged themselves in 2! ways; i.e.,2! = 2 ways

Therefore, required number of ways = 720 x 2 = 1440 ways.

Question

In how many different ways can the letters of the word "COMPLAINT" be arranged in such a way that the vowels occupy only the odd positions?

a) 1440 b) 43200 c) 1440 d) 5420

Answer : b) 43200

Solution :

There are 9 different letters in the given word "COMPLAINT", out of which there are 3 vowels and 6 consonants.

Let us mark these positions as under:

[1] [2] [3] [4] [5] [6] [7] [8] [9]

Now, 3 vowels can be placed at any of the three places out of 5 marked 1, 3, 5, 7 and 9.

Number of ways of arranging the vowels = 5P3 = 5x4x3 = 60 ways.

Also, the 6 consonants at the remaining positions may be arranged in 6P6 ways = 6! ways = 720 ways.

Therefore, required number of ways = 60 x 720 = 43200 ways.

Question

In how many different ways can the letters of the word "CANDIDATE" be arranged in such a way that the vowels always come together?

a) 4320 b) 1440 c) 720 d) 840

Answer : a) 4320

Solution :

There are 9 letters in the given word, out of which 4 are vowels.

In the word "CANDIDATE" we treat the vowels "AIAE" as one letter.

Thus, we have CNDDT(AIAE).

Now, we have to arrange 6 letters, out of which D occurs twice.

Therefore, number of ways of arranging these letters = 6!/2! = 720 / 2 = 360 ways.

Now, AIAE has 4 letters, in which A occurs 2 times and the rest are different.

Number of ways of arranging these letters = 4!/2! = 1 x 2 x 3 x 4 / 2 = 12

Therefore, required number of words = (360 x 12) = 4320.

Question

In how many different ways can the letters of the word "RADIUS" be arranged in such a way that the vowels occupy only the odd positions?

a) 72 b) 144 c) 532 d) 36

Answer : d) 36

Solution :

There are 6 different letters in the given word, out of which there are 3 vowels and 3 consonants.

Let us mark these positions as under:

[1] [2] [3] [4] [5] [6]

Now, 3 vowels can be placed at any of the three places out of 3 marked 1, 3 and 5.

Number of ways of arranging the vowels = 3P3 = 3! = 6 ways.

Also, the 3 consonants can be arranged at the remaining 3 positions.
Number of ways of these arrangements = 3P3 = 3! = 6 ways.

Therefore, total number of ways = 6 x 6 = 36.