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- Question
- In how many difference ways can six players be arranged in a line such that two of them, Abhinav and Manjesh are never together?
Options- A. 120
- B. 240
- C. 360
- D. 480
- Correct Answer
- 360
ExplanationAs, there are six players, so total ways in which they can be arranged = 6 ! ways
Also, two particular players,are never together.
? Required ways = 6!/2! = 360 - 1. In a question paper, there are four multiple choice type question. Each question has five choices with only one choice for its correct answer. What is the total number of ways in which a candidate will not get all the four answers correct?
Options- A. 19
- B. 120
- C. 624
- D. 1024 Discuss
- 2. Groups, each containing 3 boys are to be formed out of 5 boys, A, B , C, D and E such that no group can contain both C and D together. What is the maximum number of such different groups?
Options- A. 5
- B. 6
- C. 7
- D. 8 Discuss
- 3. A question paper had 10 questions. Each question could only be answered as True (T) or false (F). Each candidate answered all the questions. Yet, no two candidate wrote the answers in an identical sequence. How many different sequences of answers are possible?
Options- A. 20
- B. 40
- C. 512
- D. 1024 Discuss
- 4. How many three letter computer passwords can be formed (no repetition allowed) with at least one symmetric letter?
Options- A. 990
- B. 2730
- C. 12870
- D. 1560000 Discuss
- 5. If there are 10 positive real numbers n 1 < n 2, n 3 .... < n 10 How many triplets of these numbers (n 1, n 2, n 3) (n 2, n 3, n 4), ... can be generated such that in each triplet the first number is always less than the second number and the second number is always less the third number?
Options- A. 45
- B. 90
- C. 120
- D. 180 Discuss
- 6. A, B , C , and D are four towns, any three of which are non-collinear. Then, the number of ways to construct three roads each joining a pair of towns, so that the roads do not form a triangle, is?
Options- A. 7
- B. 8
- C. 9
- D. 24 Discuss
- 7. Three dice (each having six faces with each face having one number from 1 or 6 ) are rolled. What is the number of possible outcomes such that atleast one dice shows the numbers 2?
Options- A. 36
- B. 81
- C. 91
- D. 116 Discuss
- 8. How many different numbers can be formed from the digits 3, 4, 5, 6 and 7 when repetitions are allowed?
Options- A. 3125
- B. 625
- C. 3905
- D. 125 Discuss
- 9. Find the number of ways of arranging the host and 8 guests at a circular table, so that the host always sits in a particular seat?
Options- A. 4!
- B. 8!
- C. 6!
- D. 9! Discuss
- 10. 2 Men and 1 women board a bus in which 5 seats are vacant, one of these 5 seats is reserved for ladies. A women may or may not sit on the seat reserved for ladies . In how many different ways can the five seats be occupied by these passengers?
Options- A. 15
- B. 36
- C. 48
- D. 60 Discuss
Permutation and Combination problems
Search Results
Correct Answer: 624
Explanation:
No of multiple choice type questions = 4
Total number of ways = 5 x 5 x 5 x 5 = 625
Number of correct answer = 1
Number of false answers = 625 - 1 = 624
Correct Answer: 7
Explanation:
Maximum number of such different groups = ABC , ABD, ABE, BCE, BDE, CEA, DEA = 7
Correct Answer: 1024
Explanation:
Each question can be answered in 2 ways.
? 10 question can be answered = 210 = 1024 ways
Correct Answer: 12870
Explanation:
Total number of password using all alphabets -Total
number of password using no symmetric alphabets
= (26 x 25 x 24 ) - (15 x 14 x 13 )
= 12870
Correct Answer: 120
Explanation:
Three numbers can be selected and arranged out of 10 numbers in 10P3 ways 10!/7! = 10 x 9 x 8
Now, this arrangement is restricted to a given condition that first number is always less than the second number and second number is always than the third number. Thus, three numbers can be arranged among themselves in 3! ways.
Hence, required number of arrangement = (10 x 9 x 8)/(3 x 2)
= 120 ways
Correct Answer: 24
Explanation:
To construct 2 roads, three towns can be selected out of 4 in 4 x 3 x 2 = 24 ways. Now, if third road goes from the third town to the first town, a triangle is formed and if it goes to the fourth town, a triangle is not formed, So there are 24 ways to form a triangle and 24 ways of avoiding the formation of triangle.
Correct Answer: 91
Explanation:
When three dice are rolled, the number of possible outcomes = 63 = 216
Number of possible outcomes in which 2 does not appear on any dice = 53 = 125
? Number of possible outcomes in which atleast one dice shows 2 = 216 - 125 = 91
Correct Answer: 3905
Explanation:
Number of 1 digit numbers = 5
Number of 2 digit numbers = 52 = 25
Number of 3 digit numbers = 53 = 125
Number of 4 digit numbers = 54 = 625
Number of 5 digit numbers = 55 = 3125
? Total number of numbers formed with these digits
= 5 + 25 + 125 + 625 + 3125 = 3905
Correct Answer: 8!
Explanation:
Total number of persons = 9
Host can sit in a particular seat in one way .
Now, remaining positions are defined relative to the host .
Hence, the remaining can sit in 8 places in 8P8 = 8! ways.
? The number of required arrangements = 8! x 1 = 8! = 8! ways
Correct Answer: 36
Explanation:
Case I :-
If lady sets on reserved seat, then
2 men can occupy seats from 4 vacant seats in 4P2
= 4 x 3 = 12 ways
Case II :-
If lady does not site on reserved seat, then 1 women can occupy a seat from seat in 4 ways, 1 man can occupy a seat from 3 seats in 3 ways, also 1 man left can occupy a seat from remaining two seats in 2 ways.
? Total ways = 4 x 3 x 2 = 24 ways
Hence, from Case I and case II , total ways = 12 + 24 = 36 ways
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