bySayantani Barman Experta en el extranjero
Question: If 5 noble knights are to be seated at a round table, then how many different ways can they be seated?
- 120
- 96
- 60
- 35
- 24
Answer:
Solution with Explanation:
Approach Solution (1):
There are 5! possibilities to arrange 5 things in a row.
But since it's a round table, shifting each object to one side and putting the last at the beginning again yields the same configuration. For each possible configuration there exist 5 such rotations, because it’s 5 objects, so you have to divide the number by 5:
5! / 5 = 4!
You can also approach it by just setting one object to be the first to avoid the rotation problem which directly yields to 4!, because it's 4 objects to arrange now.
Correct Option: E
Approach Solution (2):
If the seats are distinguishable (e.g. have numbers) then 5!=120 ways, the same as the number of ways they can be placed in a row.
If the seats are not distinguishable then each of the arrangements above is counted 5 times. This can be repaired by dividing by 5 and results in 5!/5=4!=24 possibilities.
Correct Option: E
Approach Solution (3):
It depends on how we interpret the question. Five people, named A, B, C, D, E, enter a restaurant. Any one of the 5 can sit in the first chair. Any one of the remaining 4 can sit to that person’s right. Then any of the remaining 3 to that person’s right, then any of the remaining 2 to that person’s right — and the last person takes the final chair. So: 5*4*3*2*1 = 120 arrangements. However, if it doesn’t matter how the five are rotated (as in: who sits with back to the wall, or looking out the window; that is: ABCDE = BCDEA), divide by 5, so 24 arrangements.
Correct Option: E
“If 5 noble knights are to be seated at a round table, then how many different ways can they be seated?”- is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been taken from the book “GMAT Official Guide Quantitative Review”. To solve GMAT Problem Solving questions a student must have knowledge about a good amount of qualitative skills. The GMAT Quant topic in the problem-solving part requires calculative mathematical problems that should be solved with proper mathematical knowledge.
Suggested GMAT Problem Solving Samples
- Find The Altitude Of An Equilateral Triangle Whose Side is 20 GMAT Problem Solving
- Which of the following is the value of √3√0.000064? GMAT Problem Solving
- Two Dice are Thrown Simultaneously. What is the Probability of Getting Two Numbers Whose Product is Even? GMAT Problem Solving
- The Smallest 3-Digit Positive Integer Obtained By Adding Two Positive Two-Digit Numbers GMAT Problem Solving
- Train A Leaves New York at 9am Eastern Time on Monday, Headed for Los Angeles at a Constant Rate GMAT Problem Solving
- An Express Train Traveled At An Average Speed of 100 Kilometers Per Hour GMAT Problem Solving
- If m Lies Between The Integers p and s On the Number Line Shown GMAT Problem Solving
- A Cube Of Side 7 cm Is Coloured On Pair of Opposite Faces By Red, Green and Yellow Shades GMAT Problem Solving
- If x^2 − 5x − 6 = 0, which of the following could be x ? GMAT Problem Solving
- How Many Numbers Between 1 and 1000, Inclusive Have an Odd Number of Factors? GMAT Problem Solving
- GMAT Problem Solving- Given f(x) = x/(x + 1), For What Value k Does f(f(k)) = 2/3 ?
- Which Among the Following is the Smallest 7-digit Number that is Exactly Divisible by 43? GMAT Problem Solving
- During a Trip, Francine Traveled x Percent of the Total Distance at an Average Speed of 40 Miles GMAT Problem Solving
- Which of the Following Expressions CANNOT have a Negative Value? GMAT Problem Solving
- Which of the following is greatest? GMAT Problem Solving
- The Cost Price of 20 Articles is The Same as The Selling Price of x Articles GMAT Problem Solving
- In The Figure Shown, If The Area of The Shaded Region is 3 Times The Area of The Smaller Circular Region GMAT Problem Solving
- A Regular Hexagon has a Perimeter of 30 units GMAT Problem Solving
- All the Numbers 2, 3, 4, 5, 6, 7 are Assigned to the Six Faces of a Cube, One Number to Each Face GMAT Problem Solving
- If it is true that x > -2 and x < 7, which of the following must be true? GMAT Problem Solving
- In a Drawer, There are 4 White Socks, 3 Blue Socks, and 5 Grey Socks GMAT Problem Solving
- There are 100 Apples in a Bag of which 98% are Green and Rest are Red GMAT Problem Solving
- A palindrome is a number that reads the same forward and backward GMAT Problem Solving
- Three Cars Leave From A To B In Equal Time Intervals GMAT Problem Solving
- An Inlet Pipe can Fill in an Empty Cistern in 30 minutes GMAT Problem Solving
- A Zookeeper Counted the Heads of the Animals in a Zoo and Found it to be 80 GMAT Problem Solving
- A Shop Stores x kg of Rice. The First Customer Buys half this Amount Plus half a kg of Rice GMAT Problem Solving
- In a Class of 120 Students Numbered 1 to 120, All Even Numbered Students Opt for Physics GMAT Problem Solving
- Machine A Produces bolts at a Uniform Rate of 120 Every 40 seconds GMAT Problem Solving
- Out of 7 Consonants and 4 Vowels, How Many Words of 3 Consonants and 2 Vowels Can be Formed? GMAT Problem Solving
- 4 Bells Toll Together at 9:00 A.M. They Toll After 7, 8, 11 and 12 Seconds GMAT Problem Solving
- 12 Marbles are Selected at Random from a Large Collection of White, Red, Green and Yellow Marbles GMAT Problem Solving
- Find the greatest number that will divide 43, 91 and 183 GMAT Problem Solving
- Of the 150 Houses in a Certain Development GMAT Problem Solving
- A man can hit a target once in 4 shots. If he fires 4 shots in succession GMAT Problem Solving
- If 75 Percent of a Class Answered the First Question on a Certain Test Correctly GMAT Problem Solving
- A Clock Strikes 4 taking 9 seconds. GMAT Problem Solving
- What is the Largest Power of 3 Contained in 200! GMAT Problem Solving
- Find The Value Of x GMAT Problem Solving
- Which of the following expressions has the greatest values? GMAT Problem Solving
- If @ x=x^2/2x^2-2 , What is the Units Digit of @ (@4)? GMAT Problem Solving
- What is the product of all possible solutions of the equation |x+2|- 5|x+2| = -6? GMAT Problem Solving
- Metropolis Corporation has 4 Shareholders GMAT Problem Solving
- What is the number of integers from 1 to 1000, inclusive that are not divisible by 11 or by 35? GMAT Problem Solving
- If m is Three Times n, and if 2n + 3 is 20% of 25, What is the value of m? GMAT Problem Solving
- If Ben Were to Lose the Championship, Mike would be the Winner GMAT Problem Solving
- A Train Travelling at a Certain Constant Speed takes 30 seconds GMAT Problem Solving
- A conference room is equipped with a total of 45 metal or wooden chairs GMAT Problem Solving
- A welder received an order to make a 1 million litre cube-shaped tank GMAT Problem Solving
- After 6 games, Team B had an average of 61.5 points per game GMAT Problem Solving
Comments