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- Question
- 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
- Correct Answer
- 36
ExplanationCase 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 - 1. 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
- 2. 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
- 3. 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
- 4. 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
- 5. 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 Discuss
- 6. 139 person have signed for an elimination tournament. All players are to be paired up for the first round but because 139 is an odd number one player gets a bye, which promotes him to the second round without actually playing in the first round. The pairing continues on the next round with a bye to any player left over. If the schedule is planned, so that a minimum number of matches is required to determine the champion, the number of matches which must be played is?
Options- A. 136
- B. 137
- C. 138
- D. 139 Discuss
- 7. In a monthly test, the teacher decides that there will be there questions, one each from ex. 7, 8 and 9 of the text book. There are 12 questions in ex-7 , 18 in ex-8 and 9 in ex-9. In how many ways can the three questions be selected?
Options- A. 1944
- B. 2094
- C. 1894
- D. 2194 Discuss
- 8. If there are 12 persons in a party and each of them shakes hands with each other, how many handshakes do happen in the party?
Options- A. 77
- B. 66
- C. 44
- D. 55 Discuss
- 9. Find the number of ways of preparing a chain with 5 different coloured beads?
Options- A. 18
- B. 24
- C. 12
- D. 30 Discuss
- 10. Find the number of different ways of forming a committee consisting of 3 men and 3 women from 6 men and 5 women.?
Options- A. 30
- B. 20
- C. 10
- D. 25 Discuss
Permutation and Combination problems
Search Results
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: 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: 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: 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: 360
Explanation:
As, 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
Correct Answer: 138
Explanation:
Required number of member played will be (139 - 1) = 138
Correct Answer: 1944
Explanation:
Number of ways selecting 1 question from ex-7 = 12C1
Number of ways selecting 1 question from ex-8 = 18C1
Number of ways selecting 1 question from ex-9 = 9C1
? Total ways = 12C1 x 18C1 x 9C1 = 12 x 18 x 9 = 1944
Correct Answer: 66
Explanation:
first person will shake hands with 11 other persons. Seconds person will shake hands with 10 other persons, Third person will shake hands with 9 other person and so on.
So , total handshake
= 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 + 11 = 66
OR
2 person are to be chosen from 12 person to have a hand shake
? Possible ways = 12C2 = 12! / 2!(12 - 2)! = 66
Correct Answer: 12
Explanation:
Neglecting the direction of beads in the chain, number of ways of preparing a chain with 5 different coloured beads
= (1/2) x (5 -1)! = (1/2) x 4! = 24/2 = 12
Correct Answer: 30
Explanation:
The number of ways of selecting 3 men and 3 women out of 6 men and 5 women = 6C3 x 5C3
= 6!/(3! x 3!) + 5/(3! x 2!)
= 20 + 10 = 30
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