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- Question
How many ways can 10 letters be posted in 5 post boxes, if each of the post boxes can take more than 10 letters ?
Options- A. 5^10
- B. 10^5
- C. 5P5
- D. 5C5
- Correct Answer
- 5^10
ExplanationEach of the 10 letters can be posted in any of the 5 boxes.
So, the first letter has 5 options, so does the second letter and so on and so forth for all of the 10 letters.
i.e. 5*5*5*?.*5 (upto 10 times) = 5 ^ 10.
- 1. Consider the word ROTOR. Whichever way you read it, from left to right or from right to left, you get the same word. Such a word is known as palindrome. Find the maximum possible number of 5-letter palindromes.
Options- A. 17756
- B. 17576
- C. 12657
- D. 12666 Discuss
- 2. In how many different ways can the letters of the word 'DETAIL' be arranged in such a way that the vowels occupy only the odd positions?
Options- A. 36
- B. 25
- C. 42
- D. 120 Discuss
- 3. In how many ways the letters of the word 'DESIGN' can be arranged so that no consonant appears at either of the two ends?
Options- A. 240
- B. 72
- C. 48
- D. 36 Discuss
- 4. A Committee of 5 persons is to be formed from a group of 6 gentlemen and 4 ladies. In how many ways can this be done if the committee is to be included atleast one lady?
Options- A. 123
- B. 113
- C. 246
- D. 945 Discuss
- 5. In how many different ways can the letters of the word 'RITUAL' be arranged?
Options- A. 720
- B. 5040
- C. 360
- D. 180 Discuss
- 6. How many words can be formed with or without meaning by using three letters out of k, l, m, n, o without repetition of alphabets.
Options- A. 60
- B. 120
- C. 240
- D. 30 Discuss
- 7. If (1 × 2 × 3 × 4 ........ × n) = n!, then 15! - 14! - 13! is equal to ___?
Options- A. 14 × 13 × 13!
- B. 15 × 14 × 14!
- C. 14 × 12 × 12!
- D. 15 × 13 × 13! Discuss
- 8. A box contains 3 blue marbles, 4 red, 6 green marbles and 2 yellow marbles. If two marbles are picked at random, what is the probability that they are either blue or yellow ?
Options- A. 3/17
- B. 4/21
- C. 2/21
- D. 5/17 Discuss
- 9. There are 11 True or False questions. How many ways can these be answered ?
Options- A. 11!/2
- B. 1024
- C. 11!
- D. 2048 Discuss
- 10. If each vowel of the word NICELY is changed to the next letter in the English alphabetical series and each consonant is changed to the previous letter in the English alphabetical series and then the alphabets are arranged in alphabetical order, which of the following will be fourth from the left?
Options- A. M
- B. J
- C. B
- D. O Discuss
Permutation and Combination problems
Search Results
Correct Answer: 17576
Explanation:
The first letter from the right can be chosen in 26 ways because there are 26 alphabets.
Having chosen this, the second letter can be chosen in 26 ways
The first two letters can chosen in 26 x 26 = 676 ways
Having chosen the first two letters, the third letter can be chosen in 26 ways.
All the three letters can be chosen in 676 x 26 =17576 ways.
It implies that the maximum possible number of five letter palindromes is 17576 because the fourth letter is the same as the second letter and the fifth letter is the same as the first letter.
Correct Answer: 36
Explanation:
There are 6 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 4, marked 1, 3, 5.
Number of ways of arranging the vowels = = 3! = 6.
Also, the 3 consonants can be arranged at the remaining 3 positions.
Number of ways of these arrangements = = 3! = 6.
Total number of ways = (6 x 6) = 36.
Correct Answer: 48
Explanation:
DESIGN = 6 letters
No consonants appear at either of the two ends.
= = 2 x 4 x 3 x 2 x 1= 48
Correct Answer: 246
Explanation:
A Committee of 5 persons is to be formed from 6 gentlemen and 4 ladies by taking.
(i) 1 lady out of 4 and 4 gentlemen out of 6
(ii) 2 ladies out of 4 and 3 gentlemen out of 6
(iii) 3 ladies out of 4 and 2 gentlemen out of 6
(iv) 4 ladies out of 4 and 1 gentlemen out of 6
In case I the number of ways = = 4 x 15 = 60
In case II the number of ways = = 6 x 20 = 120
In case III the number of ways = = 4 x 15 = 60
In case IV the number of ways = = 1 x 6 = 6
Hence, the required number of ways = 60 + 120 + 60 + 6 = 246
Correct Answer: 720
Explanation:
The number of letters in the given word RITUAL = 6
Then,
Required number of different ways can the letters of the word 'RITUAL' be arranged = 6!
=> 6 x 5 x 4 x 3 x 2 x 1 = 720
Correct Answer: 60
Explanation:
Given letters are k, l, m, n, o = 5
number of letters to be in the words = 3
Total number of words that can be formed from these 5 letters taken 3 at a time without repetation of letters =
Correct Answer: 15 × 13 × 13!
Explanation:
15! - 14! - 13!
= (15 × 14 × 13!) - (14 × 13!) - (13!)
= 13! (15 × 14 - 14 - 1)
= 13! (15 × 14 - 15)
= 13! x 15 (14 - 1)
= 15 × 13 × 13!
Correct Answer: 2/21
Explanation:
Given that there are three blue marbles, four red marbles, six green marbles and two yellow marbles.
Probability that both marbles are blue = ³C?/¹?C? = (3 x 2)/(15 x 14) = 1/35
Probability that both are yellow = ²C?/¹?C? = (2 x 1)/(15 x 14) = 1/105
Probability that one blue and other is yellow = (³C? x ²C?)/¹?C? = (2 x 3 x 2)/(15 x 14) = 2/35
Required probability = 1/35 + 1/105 + 2/35 = 3/35 + 1/105 = 1/35(3 + 1/3) = 10/(3 x 35) = 2/21
Correct Answer: 2048
Explanation:
Given 11 questions of type True or False
Then, Each of these questions can be answered in 2 ways (True or false)
Therefore, no. of ways of answering 11 questions = = 2048 ways.
Correct Answer:
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