Question: In a conference 10 speakers are present. If S1 wants to speak before S2 and S2 wants to speak after S3, then the number of ways all the 10 speakers can give their speeches with the above restriction if the remaining seven speakers have no objection to speak at any number is

1. \(^{10}C_3\)
2. \(^{10}P_8\)
3. \(^{10}P_3\)
4. \(\frac{10!}{3}\)
5. 10!

Answer:
Solution with Explanation:
Approach Solution (1):

Pick 3 seats out of 10 and place S1, S2, and S3 in two ways due to the restrictions

\(2*^{10}C_3=2*\frac{10!}{7!*3!}\)

However, the remaining 7 speakers can get their turns to speak in 7! Ways

Total = \(2*\frac{10!}{7!*3!}*7!=\frac{10!}{3}\)

Correct Option: D

Approach Solution (2):

The 10 speakers can speak in 10! ways

However, S1 before S2 and S2 after S3 means there can be two ways S1, S3, S2 or S3, S1, S2. But they can be arranged within themselves in 3! Ways, out of which only these 2 are correct.

Thus the total has to be divided by 3! And multiplied by 2 = \(\frac{10!*2}{3!}=\frac{10!}{3}\)

Correct Option: D

“In a conference 10 speakers are present. If S1 wants to speak before S2 and S2 wants to speak after S3, then the number of ways all the 10 speakers can give their speeches with the above restriction if the remaining seven speakers have no objection to speak at any number is”- 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

• The square of \(5^\sqrt2)\ =? GMAT Problem Solving
• If 4 people are selected from a group of 6 married couples GMAT Problem Solving
• If the equation |x|+|y|= 5 encloses a certain region on the graph GMAT Problem Solving
• If x = ¾ and y = ⅖ , what is the value of (x^2+ 6x+ 9) - (y^2-2y+ 1)? GMAT Problem Solving
• There are 6 points on xy-plane GMAT Problem Solving 
• Mike, Tom, and Walt are working as sales agents for an insurance company GMAT Problem Solving 
• What is the value of k if the sum of consecutive odd integers from 1 to k equals 441? GMAT Problem Solving 
• A circle with a radius R is inscribed into a square with a side K GMAT Problem Solving 
• The square of \(5^\sqrt2)\ =? GMAT Problem Solving 
• A farm has chickens, cows and sheep GMAT Problem Solving 
• If g is an integer what is the value of (-1)^g^4-1? GMAT Problem Solving 
• What is the area of the triangle with the following vertices L(1,3) M(5,1) and N(3,5)? GMAT Problem Solving 
• A contractor estimated that his 10-man crew could complete the construction GMAT Problem Solving
• A circle is inscribed in a square with the diagonal of 4 centimeters GMAT Problem Solving
• At a dog competition, a dog is awarded 10 points if it runs through 4 pipes GMAT Problem Solving
• Two consultants, Mary and Jim, can type up a report in 12.5 hours and edit it in 7.5 hours GMAT Problem Solving
• A Man has 1044 Candles. After Burning, He can Make a New Candle 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
• 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
• 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.
• If 10, 12 and ‘x’ are Sides of an Acute Angled Triangle, How Many Integer Values of ‘x’ are Possible? GMAT Problem Solving
• \(\frac{15^{11}-15^{10}}{14}=?\) GMAT Problem Solving
• For Any Four Digit Number, abcd, *abcd*= (3^a)(5^b)(7^c)(11^d) GMAT Problem Solving
• GMAT Problem Solving - Iqbal Dealt Some Cards to Mushtaq and himself from a Full Pack of Playing Cards
• A Rectangular Box has Dimensions 12*10*8 Inches GMAT Problem Solving