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- Question
If nC10=nC12 then,find n.
Options- A. 10
- B. 12
- C. 22
- D. 24
- Correct Answer
- 22
ExplanationUsing, we get
n ? 10 = 12
or, n = 12 + 10 = 22
- 1. Find the number of ways in which 21 balls can be distributed among 3 persons such that each person does not receive less than 5 balls.
Options- A. 28
- B. 14
- C. 21
- D. 7 Discuss
- 2. How many four digits numbers greater than 6000 can be made using the digits 0, 4, 2, 6 together with repetition.
Options- A. 64
- B. 63
- C. 62
- D. 60 Discuss
- 3. Find the total numbers greater than 4000 that can be formed with digits 2, 3, 4, 5, 6 no digit being repeated in any number ?
Options- A. 120
- B. 256
- C. 192
- D. 244 Discuss
- 4. A polygon has 44 diagonals, then the number of its sides are ?
Options- A. 13
- B. 9
- C. 11
- D. 7 Discuss
- 5. A decision committee of 5 members is to be formed out of 4 Actors, 3 Directors and 2 Producers. In how many ways a committee of 2 Actors, 2 Directors and 1 Producer can be formed ?
Options- A. 18
- B. 24
- C. 36
- D. 32 Discuss
- 6. Four ladies A, B, C and D and four gentlemen E, F, G and H are sitting in a circle round a table facing each other. Directions: (1) No two ladies or two gentlemen are sitting side by side. (2) C, who is sitting between G and E is facing D. (3) F is between D and A and is facing G. (4) H is to the right of B. Question: 1. Who are immediate neighbours of B? 2. E is facing whom?
Options- A. G & H , H
- B. F & H , B
- C. E & F , F
- D. E & H , G Discuss
- 7. In How many ways is it possible to make a selection by taking any number of 15 fruits, namely 3 oranges, 5 apples and 7 mangoes?
Options- A. 131
- B. 191
- C. 68
- D. 3720 Discuss
- 8. How many different four letter words can be formed (the words need not be meaningful using the letters of the word "MEDITERRANEAN" such that the first letter is E and the last letter is R?
Options- A. 59
- B. 56
- C. 64
- D. 55 Discuss
- 9. There are 7 non-collinear points. How many triangles can be drawn by joining these points?
Options- A. 10
- B. 30
- C. 35
- D. 60 Discuss
- 10. There are 6 bowlers and 9 batsmen in a cricket club. In how many ways can a team of 11 be selected so that the team contains at least 4 bowlers?
Options- A. 1170
- B. 1200
- C. 720
- D. 360 Discuss
Permutation and Combination problems
Search Results
Correct Answer: 28
Explanation:
Let x, y, z be the number of balls received by the three persons, then
Let
x + y + z =21
u + 5 + v + 5 + w + 5 = 21
u + v + w = 6
Total number of solutions =
Correct Answer: 63
Explanation:
Given digits are 0, 4, 2, 6
Required 4 digit number should be greater than 6000.
So, first digit must be 6 only and the remaining three places can be filled by one of all the four digits.
This can be done by
1x4x4x4 = 64
Greater than 6000 means 6000 should not be there.
Hence, 64 - 1 = 63.
Correct Answer: 192
Explanation:
We are having with digits 2, 3, 4, 5 & 6 and numbers greater than 4000 are to be formed, no digit is repeated.
The number can be 4 digited but greater than 4000 or 5 digited.
Number of 4 digited numbers greater than 4000 are
4 or 5 or 6 can occupy thousand place => 3 x
= 3 x 24 = 72.
5 digited numbers = = 5! = 120
So the total numbers greater than 4000 = 72 + 120 = 192
Correct Answer: 11
Explanation:
Let the number of sides be n.
The number of diagonals is given by nC2 - n
Therefore, nC2 - n = 44, n>0
nC2 - n = 44
n2 - 3n - 88 = 0
n2 -11n + 8n - 88 = 0
n = -8 or n = 11.
As n>0, n will not be -8. Therefore, n=11.
Correct Answer: 36
Explanation:
Required Number of ways = = 36
Correct Answer: G & H , H
Correct Answer: 191
Explanation:
Out of 15 fruits, 7 are alike of one kind, 5 are alike of a second kind and 3 are alike of a third kind.
Hence, the required number of ways = [ (7+1) (5+1) (3+1) -1] =191
Correct Answer: 59
Explanation:
The first letter is E and the last one is R.
Therefore, one has to find two more letters from the remaining 11 letters.
Of the 11 letters, there are 2 Ns, 2Es and 2As and one each of the remaining 5 letters.
The second and third positions can either have two different letters or have both the letters to be the same.
Case 1: When the two letters are different. One has to choose two different letters from the 8 available different choices. This can be done in 8 * 7 = 56 ways.
Case 2: When the two letters are same. There are 3 options - the three can be either Ns or Es or As. Therefore, 3 ways.
Total number of possibilities = 56 + 3 = 59
Correct Answer: 35
Explanation:
A triangle is formed by joining any three non-collinear points in pairs.
There are 7 non-collinear points
The number of triangles formed = = 35
Correct Answer: 1170
Explanation:
Possibilities Bowlers Batsmen Number of ways
6 9
1 4 7
2 5 6
3 6 5
= 15 x 36 = 540
= 6 x 84 = 504
= 1 x 126 = 126
Total = 1170
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