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- Question
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
- Correct Answer
- 186
ExplanationWhen 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
- 1. 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
- 2. 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
- 3. 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
- 4. 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
- 5. An engineering student has to secure 36% marks to pass. He gets 53 and fails by 37 marks. Find the maximum marks.
Options- A. 275 marks
- B. 250 marks
- C. 300 marks
- D. 325 marks Discuss
- 6. 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
- 7. 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
- 8. 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
- 9. 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
- 10. 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
Permutation and Combination problems
Search Results
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: 250 marks
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: 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.
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