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1) In what ways the letters of the word "RUMOUR" can be arranged?

  1. 180
  2. 150
  3. 200
  4. 230

Answer: D

Answer with the explanation:

The word RUMOUR consists of 6 words in which R and U are repeated twice.
Therefore, the required number of permutations = Apti Permutation and Combination
Or, Apti Permutation and Combination = 180

Hence, 180 words can be formed by arranging the word RUMOUR.


2) In what ways the letters of the word "PUZZLE" can be arranged to form the different new words so that the vowels always come together?

  1. 280
  2. 450
  3. 630
  4. 240

Answer: D

Answer with the explanation:

The word PUZZLE has 6 different letters, but ATQ, the vowels should always come together.
Now, let the vowels UE as a single entity.
Therefore, the number of letters is PZZL = 4, and UE = 1
Since the total number of letters = 4+1 = 5
So the arrangement would be in 5P5 = Apti Permutation and Combination= Apti Permutation and Combination= 5! = 5*4*3*2*1 = 120 ways.

Note: we know that 0! = 1

Now, the vowels AE can arrange in 2 different ways, i.e., 2P2 = 2! = 2*1 = 2 ways

Hence, the new words that can be formed = 120 *2 = 240.


3) In what ways can a group of 6 boys and 2 girls be made out of the total of 7 boys and 3 girls?

  1. 50
  2. 120
  3. 21
  4. 20

Answer: C

Answer with the explanation:

We know that nCr = nC(n-r)

The combination of 6 boys out of 7 and 2 girls out of 3 can be represented as 7C6 + 3C2
Therefore, the required number of ways = 7C6 * 3C2 = 7C(7-6) * 3C(3-2) = Apti Permutation and Combination = 21

Hence, in 21 ways the group of 6 boys and 2 girls can be made.


4) Out of a group of 7 boys and 6 girls, five boys are selected to form a team so that at least 3 boys are there on the team. In how many ways can it be done?

  1. 645
  2. 734
  3. 756
  4. 612

Answer: C

Answer with the explanation:

We may have 5 men only, 4 men and 1 woman, and 3 men and 2 women in the committee.

So, the combination will be

as we know that

nCr= Apti Permutation and Combination

So, (7C3 * 6C2) + (7C4 * 6C1) + (7C5)
Or, Apti Permutation and Combination + Apti Permutation and Combination + Apti Permutation and Combination

Or, 525 +210+21 = 756

So, there are 756 ways to form a committee.


5) A box contains 2 red balls, 3 black balls, and 4 white balls. Find the number of ways by which 3 balls can be drawn from the box in which at least 1 black ball should be present.

  1. 64
  2. 48
  3. 32
  4. 96

Answer: A

Answer with the explanation:

The possible combination could be (1 black ball and 2 non-black balls), (2 black balls and 1 non- black ball), and (only 3 black balls).

Therefore the required number of combinations = (3C1 * 6C2) + (3C2 * 6C1) + (3C3)
r,Apti Permutation and Combination + Apti Permutation and Combination + Apti Permutation and Combination = 45+18+1 = 64


Permutation and Combination Test Paper 2
Permutation and Combination Concepts





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