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- Question
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
- Correct Answer
- 2/21
ExplanationGiven 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
- 1. 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
- 2. 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
- 3. 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
- 4. 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
- 5. 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
- 6. 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
- 7. 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
- 8. The ratio of the members of blue to red balls in abag is constant. When there were 44 red balls, the number of blue balls was 36. If the number of blue balls is 54, how many red balls will be in the bag?
Options- A. 68
- B. 32
- C. 64
- D. 66 Discuss
- 9. How many more words can be formed by using the letters of the given word 'CREATIVITY'?
Options- A. 851250
- B. 751210
- C. 362880
- D. 907200 Discuss
- 10. A box contains 5 green, 4 yellow and 5 white pearls. Four pearls are drawn at random. What is the probability that they are not of the same colour ? A) 11/91 B) 4/11 C) 1/11 D) 90/91
Options- A. Option A
- B. Option B
- C. Option C
- D. Option D Discuss
Permutation and Combination problems
Search Results
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: 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: 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: 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: 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:
Correct Answer: 66
Correct Answer: 907200
Explanation:
The number of letters in the given word CREATIVITY = 10
Here T & I letters are repeated
=> Number of Words that can be formed from CREATIVITY = 10!/2!x2! = 3628800/4 = 907200
Correct Answer: Option D
Explanation:
Let S be the sample space. Then,
n(s) = number of ways of drawing 4 pearls out of 14
=
ways =
= 1001
Let E be the event of drawing 4 pearls of the same colour.
Then, E = event of drawing (4 pearls out of 5) or (4 pearls out of 4) or (4 pearls out of 5)
= 5+1+5 =11
P(E) =
Required probability =
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