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- Question
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
- Correct Answer
- 246
ExplanationA 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
- 1. In how many different ways can the letters of the word 'RITUAL' be arranged?
Options- A. 720
- B. 5040
- C. 360
- D. 180 Discuss
- 2. A card is drawn from a pack of 52 cards. What is the probability that either card is black or a king?
Options- A. 15/52
- B. 17/26
- C. 13/17
- D. 15/26 Discuss
- 3. From a bunch of flowers having 16 red roses and 14 white roses, four flowers have to be selected. In how many different ways can they be selected such that at least one red rose is selected?
Options- A. 27405
- B. 26584
- C. 26585
- D. 27404 Discuss
- 4. On the occasion of New Year, each student of a class sends greeting cards to the others. If there are 21 students in the class, what is the total number of greeting cards exchanged by the students?
Options- A. 380
- B. 420
- C. 441
- D. 400 Discuss
- 5. How many six digit odd numbers can be formed from the digits 0, 2, 3, 5, 6, 7, 8, and 9 (repetition not allowed)?
Options- A. 8640
- B. 720
- C. 3620
- D. 4512 Discuss
- 6. 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
- 7. 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
- 8. 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
- 9. 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 Discuss
- 10. 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
Permutation and Combination problems
Search Results
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: 15/26
Explanation:
Number of cards in a pack of cards = 52
Number of black cards = 26
Number of king cards = 4 (2 Red, 2 Black)
Required, the probability that if a card is drawn either card is black or a king =
Correct Answer: 27404
Explanation:
Given total 16 Red roses and 14 White roses = 30 roses
Four flowers have to be selected from 30 i.e, = 27405 Ways
Now, atleast one Red rose is selected i.e, 27405(total) - 1(all four are white roses) = 27404 ways.
Correct Answer: 420
Explanation:
Given total number of students in the class = 21
So each student will have 20 greeting cards to be send or receive (21 - 1(himself))
Therefore, the total number of greeting cards exchanged by the students = 20 x 21 = 420.
Correct Answer: 8640
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: 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: 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: 5^10
Explanation:
Each 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.
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 =
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