Discussion
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- Question
- From a group of 6 men and 4 women a committee of 4 persons is to be formed?
Options- A. 210
- B. 225
- C. 195
- D. 185
- Correct Answer
- 195
ExplanationRequired no. of ways = [4C1 x 6C3] + [4C2 x 6C2] + [4C3 x 6C1] + [4C4]
= 80 + 90 + 24 + 1 = 195. - 1. From 4 officers and 8 Jawans in how many ways can 6 be chosen to include at least one officer?
Options- A. 896
- B. 986
- C. 886
- D. 996 Discuss
- 2. In how many different ways can the letters of word JUDGE be arranged so that the vowels always come together?
Options- A. 48
- B. 24
- C. 120
- D. 60 Discuss
- 3. If 7 points out of 12 are in the same straight line, then the number of triangles formed is?
Options- A. 19
- B. 158
- C. 185
- D. 201 Discuss
- 4. If S= {2, 3, 4, 5, 7, 9} , then the number of different three-digit number (with all distinct digits) less than 400 that can be formed from S is?
Options- A. 20
- B. 40
- C. 80
- D. 120 Discuss
- 5. If nP r= 720 nC r than the value r is?
Options- A. 6
- B. 5
- C. 4
- D. 7 Discuss
- 6. The numbers of straight lines can be formed out of 10 points of which 7 are collinear?
Options- A. 26
- B. 21
- C. 25
- D. None of these Discuss
- 7. The number of different permutations of the word 'BANANA' is?
Options- A. 270
- B. 60
- C. 120
- D. 360 Discuss
- 8. Everybody in a room shakes hands with everybody else. The total number of hand shakes is 66. The total number of persons in the room is?
Options- A. 11
- B. 12
- C. 13
- D. 14 Discuss
- 9. In how many ways can the letter of the word ' civilization' be arranged?
Options- A. 12! / 4!
- B. 12! / 4! -1
- C. 13! / 5! - 1
- D. None of these Discuss
- 10. Letters of the word DIRECTOR are arranged in such a way that all the vowels come together. Find out the total no. of ways for making such arrangement.?
Options- A. 4320
- B. 2720
- C. 2160
- D. 1120 Discuss
Permutation and Combination problems
Search Results
Correct Answer: 896
Explanation:
We may choose 1 officer and 5 jawans or 2 officers and 4 jawans ......... or 4 officers and 2 jawans.
So Required answer = [4C1 x 8C5] + [4C2 x 8C4] + [4C3 x 8C3] + [4C4 x 8C2]
= 224 + 420 + 224 + 28 = 896.
Correct Answer: 48
Explanation:
Total number of letters = 5
Number of vowels = 2.
If we consider both vowel as a one letter then,
Required number = 4! 2! = 48.
Correct Answer: 185
Explanation:
The number of ways of selecting 3 points out of 12 points is 12C3. The number of ways of selecting 3 points out of 7 points, on the same straight line is 7C3, Hence, the number of triangle formed will be 12C3 - 7C3 = 210 - 35 = 185.
Correct Answer: 20
Explanation:
The hundred place will be reserved for 3 or 2
5 digits are free to fill rest two places i,e., of tens and unit.
Number of required 3 digit number = 2 x 5C2 = 20
Correct Answer: 6
Explanation:
We know that, nPr = nCrr!
? nPr = 720nCr
? nCr.r! = 720nCr
? r! = 720
? r = 6
Correct Answer: 25
Explanation:
If there were no three points collinear. We should have 10C2 lines but since 7 points are collinear we must subtract 7C2 lines and add the one corresponding to the line of collinearity of the seven points.
Thus, the required number of straight lines .
= 10C2 - 7C2 + 1 = 25
Correct Answer: 60
Explanation:
There are 3A's 2N's and one B. We have to find the total number of arrangements of 6 letters out of which 3 are alike of one kind, 2 are alike of second kind, thus the total number of words
= 6! / (3! 2!) = 60
Correct Answer: 12
Explanation:
Let there be n persons in the room. The total number of hand shakes is same as the number of ways of selecting 2 out of n.
nC2 = 66
? n(n - 1) / 2! = 66
? n2 - n - 132 = 0
? (n - 12) (n + 11) = 0
? n = 12
Correct Answer: 12! / 4! -1
Explanation:
There are 12 letters in the world 'civilization' of which four are i's and other are different letters.
? Total number of permutations = 12!/4!
But one word is civilization itself.
? Required number of rearrangements = 12!/4! - 1
Correct Answer: 2160
Explanation:
Taping all vowels (IEO) as a single letter (since they come together ) there are six letters with two 'R' s
Hence no. of arrangement = 6!/2! x 3! = 2160
[3 vowels can be arranged in 3! ways among themselves, here multiplied with 3!. ]
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