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- Question
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
- Correct Answer
- 3
ExplanationYou 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.
- 1. 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
- 2. 12 people at a party shake hands once with everyone else in the room.How many handshakes took place?
Options- A. 72
- B. 66
- C. 76
- D. 64 Discuss
- 3. If the letters of the word SACHIN are arranged in all possible ways and these words are written out as in dictionary, then the word ?SACHIN? appears at serial number :
Options- A. 601
- B. 600
- C. 603
- D. 602 Discuss
- 4. A committee of 5 persons is to be formed from 6 men and 4 women. In how many ways can this be done when at least 2 women are included ?
Options- A. 196
- B. 186
- C. 190
- D. 200 Discuss
- 5. How many integers, greater than 999 but not greater than 4000, can be formed with the digits 0, 1, 2, 3 and 4, if repetition of digits is allowed?
Options- A. 376
- B. 375
- C. 500
- D. 673 Discuss
- 6. 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
- 7. 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
- 8. 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
- 9. 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 Discuss
- 10. 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
Permutation and Combination problems
Search Results
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: 66
Explanation:
There are 12 people, so this is our n value.
So, 1= 66
Correct Answer: 601
Explanation:
If the word started with the letter A then the remaining 5 positions can be filled in 5! Ways.
If it started with c then the remaining 5 positions can be filled in 5! Ways.Similarly if it started with H,I,N the remaining 5 positions can be filled in 5! Ways.
If it started with S then the remaining position can be filled with A,C,H,I,N in alphabetical order as on dictionary.
The required word SACHIN can be obtained after the 5X5!=600 Ways i.e. SACHIN is the 601th letter.
Correct Answer: 186
Explanation:
When at least 2 women are included.
The committee may consist of 3 women, 2 men : It can be done in ways
or, 4 women, 1 man : It can be done in ways
or, 2 women, 3 men : It can be done in ways.
Total number of ways of forming the committees
=
= 6 x 20 + 4 x 15 + 1x 6
= 120 + 60 + 6 =186
Correct Answer: 376
Explanation:
The smallest number in the series is 1000, a 4-digit number.
The largest number in the series is 4000, the only 4-digit number to start with 4.
The left most digit (thousands place) of each of the 4 digit numbers other than 4000 can take one of the 3 values 1 or 2 or 3.
The next 3 digits (hundreds, tens and units place) can take any of the 5 values 0 or 1 or 2 or 3 or 4.
Hence, there are 3 x 5 x 5 x 5 or 375 numbers from 1000 to 3999.
Including 4000, there will be 376 such numbers.
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: 63
Explanation:
Required number of ways =
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: 43200
Explanation:
There 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
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.
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