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- Question
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
- Correct Answer
- 601
ExplanationIf 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.
- 1. 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
- 2. 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
- 3. Out of 7 consonants and 4 vowels, how many words of 3 consonants and 2 vowels can be formed?
Options- A. 25200
- B. 52000
- C. 120
- D. 24400 Discuss
- 4. If the selling price of an item is Rs 1150 after getting a discount of 8%, what is its marked price?
Options- A. Rs 1250
- B. Rs 1242
- C. Rs 1058
- D. Rs 1064 Discuss
- 5. An engineering student has to secure 25% marks to pass. He gets 47 and fails by 43 marks. What are the maximum marks of the examination?
Options- A. 385 marks
- B. 410 marks
- C. 360 marks
- D. 435 marks Discuss
- 6. 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
- 7. 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
- 8. 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
- 9. 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
- 10. 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
Permutation and Combination problems
Search Results
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: 25200
Explanation:
Number of ways of selecting (3 consonants out of 7) and (2 vowels out of 4) = ( * )
= 210.
Number of groups, each having 3 consonants and 2 vowels = 210.
Each group contains 5 letters.
Number of ways of arranging 5 letters among themselves = 5! = 120
Required number of ways = (210 x 120) = 25200.
Correct Answer: Rs 1250
Correct Answer: 360 marks
Correct Answer: 66
Explanation:
There are 12 people, so this is our n value.
So, 1= 66
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: 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 '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 =
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