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- Question
How many alphabets need to be there in a language if one were to make 1 million distinct 3 digit initials using the alphabets of the language?
Options- A. 1000
- B. 100
- C. 500
- D. 999
- Correct Answer
- 100
Explanation1 million distinct 3 digit initials are needed.
Let the number of required alphabets in the language be ?n?.
Therefore, using ?n? alphabets we can form n * n * n = distinct 3 digit initials.
Note distinct initials is different from initials where the digits are different.
For instance, AAA and BBB are acceptable combinations in the case of distinct initials while they are not permitted when the digits of the initials need to be different.
This different initials = 1 million
i.e. (1 million = )
=> n = = 100
Hence, the language needs to have a minimum of 100 alphabets to achieve the objective.
- 1. There are 4 books on fairy tales, 5 novels and 3 plays. In how many ways can you arrange these so that books on fairy tales are together, novels are together and plays are together and in the order, books on fairytales, novels and plays ?
Options- A. 12400
- B. 17820
- C. 17280
- D. 12460 Discuss
- 2. In a plane 8 points are colliner out of 12 points, then the number of triangles we get with those 12 points is
Options- A. 20
- B. 160
- C. 164
- D. 220 Discuss
- 3. From a group of 7 boys and 6 girls, five persons are to be selected to form a team, so that at least 3 girls are there in the team. In how many ways can it be done?
Options- A. 427
- B. 531
- C. 651
- D. 714 Discuss
- 4. The number of ways in which six boys and six girls can be seated in a row for a photograph so that no two girls sit together is ?
Options- A. 2(6!)
- B. 6! x 7
- C. 6! x ?P?
- D. None Discuss
- 5. How many three digit numbers 'abc' are formed where two of the three digits are same ?
Options- A. 252
- B. 648
- C. 243
- D. 900 Discuss
- 6. A polygon 7 sides.How many diagonals can be formed?
Options- A. 14
- B. 7
- C. 15
- D. 21 Discuss
- 7. If there are 15 dots on a circle,how many triangles can be formed?
Options- A. 455
- B. 450
- C. 469
- D. 500 Discuss
- 8. When six fairs coins are tossed simultaneously, in how many of the outcomes will at most three of the coins turn up as heads ?
Options- A. 15
- B. 42
- C. 16
- D. 40 Discuss
- 9. There are eight boxes of chocolates, each box containing distinct number of chocolates from 1 to 8. In how many ways four of these boxes can be given to four persons (one boxes to each) such that the first person gets more chocolates than each of the three, the second person gets more chocolates than the third as well as the fourth persons and the third person gets more chocolates than fourth person?
Options- A. 70
- B. 40
- C. 72
- D. 80 Discuss
- 10. If the letters of the word VERMA are arranged in all possible ways and these words are written out as in a dictionary, then the rank of the word VERMA is :
Options- A. 108
- B. 117
- C. 810
- D. 180 Discuss
Permutation and Combination problems
Search Results
Correct Answer: 17280
Explanation:
There are 4 books on fairy tales and they have to be put together. They can be arranged in 4! ways.
Similarly, there are 5 novels.They can be arranged in 5! ways.
And there are 3 plays.They can be arranged in 3! ways.
So, by the counting principle all of them together can be arranged in 4!´5!´3! ways = 17280
Correct Answer: 164
Explanation:
For a triangle, we need 3 non-collinear points. So with 12 points (when all the 12 are such that any three non-collinear is . But among them 8 points are collinear.
If all these 8 points are different we get triangles as they are collinear.
In triangles, we do not get triangles
Therefore, The number of triangles we get = = 164
Correct Answer: 531
Explanation:
Given in the question that, there are 7 boys and 6 girls.
Team members = 5
Now, required number of ways in which a team of 5 having atleast 3 girls in the team =
Correct Answer: 6! x ?P?
Explanation:
We can initially arrange the six boys in 6! ways.
Having done this, now three are seven places and six girls to be arranged. This can be done in ?P? ways.
Hence required number of ways = 6! x ?P?
Correct Answer: 243
Explanation:
Digits are 0,1,2,3,4,5,6,7,8,9. So no. of digits are 10
First all possible case => 9(0 excluded) x 10 x 10 = 900
Second no repetition allowed =>9 x 9 x 8 = 648
Third all digits are same => 9 (111,222,333,444,555,666,777,888,999)
Three digit numbers where two of the three digits are same = 900 - 648 - 9 = 243 ;
Correct Answer: 14
Explanation:
- 7 = 14
Correct Answer: 455
Explanation:
There are 15 dots in total,and to make a triangle we need to select any three of those dots.
So, = 455
Correct Answer: 42
Explanation:
The question requires you to find number of the outcomes in which at most 3 coins turn up as heads.
i.e., 0 coins turn heads or 1 coin turns head or 2 coins turn heads or 3 coins turn heads.
The number of outcomes in which 0 coins turn heads is =1
The number of outcomes in which 1 coin turns head is = =6
The number of outcomes in which 2 coins turn heads is =15
The number of outcomes in which 3 coins turn heads is =20
Therefore, total number of outcomes =1+6+15+20= 42 outcomes
Correct Answer: 70
Explanation:
All the boxes contain distinct number of chocolates.
For each combination of 4 out of 8 boxes, the box with the greatest number has to be given to the first person, the box with the second highest to the second person and so on.
The number of ways of giving 4 boxes to the 4 person is: 8 = 70
Correct Answer: 108
Explanation:
The number of words beign with A is 4!
The number of words beign with E is 4!
The number of words beign with M is 4!
The number of words beign with R is 4!
Number of words beign with VA is 3!
Words beign with VE are VEAMR
VEARM
VEMAR
VEMRA
VERAM
VERMA
Therefore, The Rank of the word VERMA = 4 x 4! + 3! + 6 = 96 + 6 + 6 =108
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