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- Question
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
- Correct Answer
- 243
ExplanationDigits 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 ;
- 1. Some children goto ice-cream shop. 9 flavours are available there. Each child takes a cone with two different flavours. No two children take same combination and they have taken all such possible combinations. How many children went to ice cream shop ?
Options- A. 28
- B. 56
- C. 44
- D. 36 Discuss
- 2. There are 3 sections with 5 questions each. If four questions are selected from each section, the chance of getting different questions is ?
Options- A. 1000
- B. 625
- C. 525
- D. 125 Discuss
- 3. A Cricket team of 23 people all shake hands with each other exactly once. How many hand shakes occur ?
Options- A. 142
- B. 175
- C. 212
- D. 253 Discuss
- 4. The number of signals that can be generated by using 5 differently coloured flags, when any number of them may be hoisted at a time is:
Options- A. 235
- B. 253
- C. 325
- D. None of these Discuss
- 5. If a+b+c = 21, what is the total number of non - negative integral solutions?
Options- A. 123
- B. 253
- C. 321
- D. 231 Discuss
- 6. 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
- 7. 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
- 8. 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
- 9. 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
- 10. 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 Discuss
Permutation and Combination problems
Search Results
Correct Answer: 36
Explanation:
Given there are 9 flavours of ice creams.
Each child takes the combination of two flavours and no two children will have the same combination
This can be done by ways i.e children.
Number of children= = 9 x 8 / 1x 2 = 36.
Correct Answer: 125
Explanation:
Methods for selecting 4 questions out of 5 in the first section = 5 x 4 x 3 x 2 x 1/4 x 3 x 2 x 1 = 5. Similarly for other 2 sections also i.e 5 and 5
So total methods = 5 x 5 x 5 = 125.
Correct Answer: 253
Explanation:
The first person shakes hands with 22 different people, the second person also shakes hands with 22 different people, but one of those handshakes was counted in the 22 for the first person, so the second person actually shakes hands with 21 new people. The third person, 20 people, and so on...
So,
22 + 21 + 20 + 19 + 18 + 17 + 16 + 15 + 14 + 13 + 12 + 11 + 10 + 9 + 8 + 7 + 6 + 5 + 4 + 3 + 2 + 1
= n(n+1)/2 = 22 x 23 /2 = 11 x 23 = 253.
Correct Answer: 325
Explanation:
Required number of signals =
= 5 + 20 + 60 + 120 + 120 = 325
Correct Answer: 253
Explanation:
Number of non - negative integral solutions = = 253
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: 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: 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: 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: 100
Explanation:
1 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.
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