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- Question
How many arrangements can be made out of the letters of the word COMMITTEE, taken all at a time, such that the four vowels do not come together?
Options- A. 216
- B. 45360
- C. 1260
- D. 43200
- Correct Answer
- 43200
ExplanationThere are total 9 letters in the word COMMITTEE in which there are 2M's, 2T's, 2E's.
The number of ways in which 9 letters can be arranged = = 45360
There are 4 vowels O,I,E,E in the given word. If the four vowels always come together, taking them as one letter we have to arrange 5 + 1 = 6 letters which include 2Ms and 2Ts and this be done in = 180 ways.
In which of 180 ways, the 4 vowels O,I,E,E remaining together can be arranged in = 12 ways.
The number of ways in which the four vowels always come together = 180 x 12 = 2160.
Hence, the required number of ways in which the four vowels do not come together = 45360 - 2160 = 43200
- 1. A college has 10 basketball players. A 5-member team and a captain will be selected out of these 10 players. How many different selections can be made?
Options- A. 1260
- B. 1400
- C. 1250
- D. 1600 Discuss
- 2. In how many ways can a group of 5 men and 2 women be made out of a total of 7 men and 3 women?
Options- A. 135
- B. 63
- C. 125
- D. 64 Discuss
- 3. In how many different ways can the letters of the word 'OPTICAL' be arranged so that the vowels always come together?
Options- A. 360
- B. 700
- C. 720
- D. 120 Discuss
- 4. How many lines can you draw using 3 non collinear (not in a single line) points A, B and C on a plane?
Options- A. 3
- B. 6
- C. 2
- D. 4 Discuss
- 5. In how many different ways can the letters of the word 'LEADING' be arranged in such a way that the vowels always come together?
Options- A. 720
- B. 520
- C. 700
- D. 750 Discuss
- 6. How many 4-letter words with or without meaning, can be formed out of the letters of the word, 'LOGARITHMS', if repetition of letters is not allowed?
Options- A. 4050
- B. 3600
- C. 1200
- D. 5040 Discuss
- 7. When four fair dice are rolled simultaneously, in how many outcomes will at least one of the dice show 3?
Options- A. 620
- B. 671
- C. 625
- D. 567 Discuss
- 8. In a Plane there are 37 straight lines, of which 13 pass through the point A and 11 pass through the point B. Besides, no three lines pass through one point, no lines passes through both points A and B , and no two are parallel. Find the number of points of intersection of the straight lines.
Options- A. 525
- B. 535
- C. 545
- D. 555 Discuss
- 9. How many necklace of 12 beads each can be made from 18 beads of different colours?
Options- A. 18!
- B. 18! x 19!
- C. 18!(6 x 24)
- D. 18! x 30 Discuss
- 10. How many 7 digit numbers can be formed using the digits 1, 2, 0, 2, 4, 2, 4?
Options- A. 120
- B. 360
- C. 240
- D. 424 Discuss
Permutation and Combination problems
Search Results
Correct Answer: 1260
Explanation:
A team of 6 members has to be selected from the 10 players. This can be done in or 210 ways.
Now, the captain can be selected from these 6 players in 6 ways.
Therefore, total ways the selection can be made is 210×6= 1260
Correct Answer: 63
Explanation:
Required number of ways =
Correct Answer: 720
Explanation:
The word 'OPTICAL' contains 7 different letters.
When the vowels OIA are always together, they can be supposed to form one letter.
Then, we have to arrange the letters PTCL (OIA).
Now, 5 letters can be arranged in 5! = 120 ways.
The vowels (OIA) can be arranged among themselves in 3! = 6 ways.
Required number of ways = (120 x 6) = 720.
Correct Answer: 3
Explanation:
You need two points to draw a line. The order is not important. Line AB is the same as line BA. The problem is to select 2 points out of 3 to draw different lines. If we proceed as we did with permutations, we get the following pairs of points to draw lines.
AB , AC
BA , BC
CA , CB
There is a problem: line AB is the same as line BA, same for lines AC and CA and BC and CB.
The lines are: AB, BC and AC ; 3 lines only.
So in fact we can draw 3 lines and not 6 and that's because in this problem the order of the points A, B and C is not important.
Correct Answer: 720
Explanation:
The word 'LEADING' has 7 different letters.
When the vowels EAI are always together, they can be supposed to form one letter.
Then, we have to arrange the letters LNDG (EAI).
Now, 5 (4 + 1) letters can be arranged in 5! = 120 ways.
The vowels (EAI) can be arranged among themselves in 3! = 6 ways.
Required number of ways = (120 x 6) = 720.
Correct Answer: 5040
Explanation:
'LOGARITHMS' contains 10 different letters.
Required number of words = Number of arrangements of 10 letters, taking 4 at a time.
=
= 5040.
Correct Answer: 671
Explanation:
When 4 dice are rolled simultaneously, there will be a total of 6 x 6 x 6 x 6 = 1296 outcomes.
The number of outcomes in which none of the 4 dice show 3 will be 5 x 5 x 5 x 5 = 625 outcomes.
Therefore, the number of outcomes in which at least one die will show 3 = 1296 ? 625 = 671
Correct Answer: 535
Explanation:
The number of points of intersection of 37 lines is . But 13 straight lines out of the given 37 straight lines pass through the same point A.
Therefore instead of getting points, we get only one point A. Similarly 11 straight lines out of the given 37 straight lines intersect at point B. Therefore instead of getting points, we get only one point B.
Hence the number of intersection points of the lines is = 535
Correct Answer: 18!(6 x 24)
Explanation:
Here clock-wise and anti-clockwise arrangements are same.
Hence total number of circular?permutations: =
Correct Answer: 360
Explanation:
There are 7 digits 1, 2, 0, 2, 4, 2, 4 in which 2 occurs 3 times, 4 occurs 2 times.
Number of 7 digit numbers = = 420
But out of these 420 numbers, there are some numbers which begin with '0' and they are not 7-digit numbers. The number of such numbers beginning with '0'.
= = 60
Hence the required number of 7 digits numbers = 420 - 60 = 360
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