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- Question
How many 3-digit numbers can be formed from the digits 2, 3, 5, 6, 7 and 9 which are divisible by 5 and none of the digits is repeated ?
Options- A. 15
- B. 20
- C. 5
- D. 10
- Correct Answer
- 20
ExplanationSince each number to be divisible by 5, we must have 5 0r 0 at the units place. But in given digits we have only 5.
So, there is one way of doing it.
Tens place can be filled by any of the remaining 5 numbers.So, there are 5 ways of filling the tens place.
The hundreds place can now be filled by any of the remaining 4 digits. So, there are 4 ways of filling it.
Required number of numbers = (1 x 5 x 4) = 20.
- 1. 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
- 2. 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
- 3. 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
- 4. 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
- 5. 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
- 6. Out of seven consonants and 4 vowels, how many words of 3 consonants and 2 vowels can be formed ?
Options- A. 25200
- B. 25000
- C. 25225
- D. 24752 Discuss
- 7. A class has 8 football players. A 5-member team and a captain will be selected out of these 8 players. How many different selections can be made ?
Options- A. 210
- B. 168
- C. 1260
- D. 10!/6! Discuss
- 8. 36 identical books must be arranged in rows with the same number of books in each row. Each row must contain at least three books and there must be at least three rows. A row is parallel to the front of the room. How many different arrangements are possible ?
Options- A. 5
- B. 6
- C. 7
- D. 8 Discuss
- 9. How many numbers of five digits can be formed by using the digits 1, 0, 2, 3, 5, 6 which are between 50000 and 60000 without repeating the digits?
Options- A. 120
- B. 240
- C. 256
- D. 360 Discuss
- 10. In a group of 6 boys and 4 girls, four children are to be selected. In how many different ways can they be selected such that at least one boy should be there?
Options- A. 209
- B. 290
- C. 200
- D. 208 Discuss
Permutation and Combination problems
Search Results
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 =
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: 66
Correct Answer:
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: 25200
Explanation:
Number of ways of selecting (3 consonants out of 7) and (2 vowels out of 4) =( ) = 210.
Number of groups, each having 3 consonants and 2 vowels =210
Each group contains 5 letters.
Number of ways of arranging 5 letters among themselves = 5! = 120.
Required number of words = (210 x 120) = 25200.
Correct Answer: 168
Explanation:
we can select the 5 member team out of the 8 in 8C5 ways = 56 ways.
The captain can be selected from amongst the remaining 3 players in 3 ways.
Therefore, total ways the selection of 5 players and a captain can be made = 56x3 = 168 ways.
(or)
Alternatively, A team of 6 members has to be selected from the 8 players. This can be done in 8C6 or 28 ways.
Now, the captain can be selected from these 6 players in 6 ways.
Therefore, total ways the selection can be made is 28x6 = 168 ways.
Correct Answer: 5
Explanation:
The following arrangements satisfy all 3 conditions.
Arrangement 1: 3 books in a row; 12 rows.
Arrangement 2: 4 books in a row; 9 rows.
Arrangement 3: 6 books in a row; 6 rows.
Arrangement 4: 9 books in a row; 4 rows.
Arrangement 5: 12 books in a row; 3 rows.
Therefore, the possible arrangements are 5.
Correct Answer: 120
Explanation:
Required number of 5 digit numbers can be formed by using the digits 1, 0, 2, 3, 5, 6 which are between 50000 and 60000 without repeating the digits are
5 x 4 x 3 x 2 x 1 = 120.
Correct Answer: 209
Explanation:
We may have (1 boy and 3 girls) or (2 boys and 2 girls) or (3 boys and 1 girl) or (4 boys).
Required number of ways =
= = 209.
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