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- Question
- The number of triangles that can be formed by choosing the vertices from a set of 12 points, seven of which lie on the same straight line, is?
Options- A. 185
- B. 175
- C. 115
- D. 105
- Correct Answer
- 185
ExplanationRequired no. of triangles = 12C3 - 7C3 = 185
- 1. A library has 'a' copies of one book, 'b' copies of each of two book, 'c' copies of each of three books and single copy of 'd' book. The number of ways in which these books can be distribute is?
Options- A. (a + b + c + d)! / (a! b! c!)
- B. (a + 2b + 3c + d)! / {a! (b!)2 (c!)3}
- C. (a + 2b + 3c + d )! / (a! b! c!)
- D. None of these Discuss
- 2. How many straight lines can be drawn from 15 non-collinear points?
Options- A. 105
- B. 120
- C. 110
- D. 115 Discuss
- 3. In a meeting between two countries, each country has 12 delegates. All the delegates of one country shake hands with all delegates of the other country. Find the number of handshakes possible?
Options- A. 72
- B. 144
- C. 288
- D. 234 Discuss
- 4. In how many different ways, can the letters of the word 'VENTURE' be arranged?
Options- A. 840
- B. 5040
- C. 1260
- D. 2520 Discuss
- 5. In how many different ways, the letters of word 'FINANCE' can be arranged?
Options- A. 5040
- B. 2040
- C. 2510
- D. 4080 Discuss
- 6. How many words of 4 consonants and 3 vowels can be made from 12 consonants and 4 vowels. If all the letters are different?
Options- A. 251820
- B. 258120
- C. 281520
- D. 285120 Discuss
- 7. 12 persons are to be arranged to a round table. If two particular persons among them are not to be side by side, the total number of arrangements is?
Options- A. 9 (10!)
- B. 2 (10!)
- C. 45 (8!)
- D. 10! Discuss
- 8. The total number of selections of fruit which can be made from 3 bananas, 4 apples and 2 oranges is?
Options- A. 39
- B. 315
- C. 512
- D. None of these Discuss
- 9. The total number of arrangements of the letters in the expression a 3b 2c 4 when written at full length is?
Options- A. 1260
- B. 2520
- C. 610
- D. None of these Discuss
- 10. If nC r - 1 = 36, nC r = 84 and nC r + 1 = 126 then?
Options- A. n = 8, r = 4
- B. n = 9, r = 3
- C. n = 7, r = 5
- D. None of these Discuss
Permutation and Combination problems
Search Results
Correct Answer: (a + 2b + 3c + d)! / {a! (b!)2 (c!)3}
Explanation:
Total number of books = a + 2b + 3c + d . Since there are 'b' copies of each of two books, 'c' copies of each of three books and single copy of 'd' book.
Therefore, the total number of arrangements is = (a + 2b + 3c + d )! / {a! (b!)2 (c!)3}
Correct Answer: 105
Explanation:
Required number of lines = nC2
= 15C2
= (15 x 14)/2
= 105
Correct Answer: 144
Explanation:
Total number of handshakes = 12 x 12 = 144
Correct Answer: 2520
Explanation:
The required different ways = 7 ! / 2 !
= 7 x 6 x 5 x 4 x 3 x 2!/2!
= 2520
Correct Answer:
Explanation:
Total number of letters = 7, but N has come twice.
So, required number of arrangements = 7 ! / 2 !
= [7 x 6 x 5 x 4 x 3 x 2! ] / 2!
= 2520
Correct Answer: 285120
Explanation:
Required no. of words = 12P4 x 4P3
= 12 x 11 x 10 x 9 x 4 x 3 x 2
= 120(100 - 1) x 24
= 288000 - 2880
= 285120
Correct Answer: 9 (10!)
Explanation:
12 persons can be seated around a round table in 11! ways. The total number of ways in which 2 particular persons sit side by side = 10! x 2!.
Hence, the required number of arrangements = 11! - 10! x 2! = 9 x (10!)
Correct Answer: None of these
Explanation:
Required number of ways = (2 + 1) (3 + 1) (4 + 1) - 1 = 59
Correct Answer: 1260
Explanation:
We have 9 letters 3 a's, 2 b's and 4 c's. These 9 letters can be arranged in 9! / (3! 2! 4!) = 1260 ways.
Correct Answer: n = 9, r = 3
Explanation:
nCr - 1 = 36, nCr = 84 and nCr + 1 = 126
? nCr / nCr - 1 = 84/36
? 3n - 10r + 3 = 0 ....(i)
nCr + 1 / nCr = 126/84
? 2n - 5r - 3 = 0 .............(ii)
From (i) and (ii) r = 3, n = 9
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