A Box Contains Two White Balls, Three Black Balls And Four Red Balls GMAT Problem Solving

Question: A box contains two white balls, three black balls and four red balls. In how many ways can three balls be drawn from the box, if at least one black ball is to be included in the draw?

1. 16
2. 32
3. 64
4. 96
5. 128

Correct Answer: (C)

Solutions and Explanation

Approach Solution - 1 :

There are nine balls total ( 2W, 3B,4R)

The total number of ways to choose 3 balls from a set of 9 balls is 9C3 = (9*8*7) / (3*2*1) = 84
The total number of ways to choose from among the white or red balls when there isn't a black ball already picked = 2W + 4R = 6C3 = 20
Therefore the total number of selection options for three balls with at least one black ball present = 84 -20 = 64

Approach Solution - 2 :

Scenario-1 :

1 Black Ball & 2 Other balls
=> 3c1 * 6c2 = 3*15 = 45

Scenario-2 :

2 Black Balls & 1 Other ball
=> 3c2*6c1 = 3*6 = 18

Scenario-3 :

3 Black Balls
3c3 = 1

As a result, the total number of selection options for three balls with at least one black ball present = 45+18+1 = 64.

“A box contains two white balls, three black balls and four red balls” - is a subject covered in the GMAT quantitative reasoning section. A student needs to be knowledgeable in a wide range of qualitative skills in order to successfully complete GMAT Problem Solving questions. There are 31 questions in the GMAT Quant section overall. Calculative mathematical problems must be solved in the GMAT quant topics' problem-solving section using appropriate mathematical skills.

Suggested GMAT Problem Solving Samples

• The Figure Below Shows a Square Inscribed in a Circle with the Radius of√6. What is the Area of the Shaded Region? 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
• Machine A can do a certain job in 12 days working 2 full shifts while Machine B can do the same job in 15 days working 2 full shifts GMAT Problem Solving
• The square of \(5^\sqrt2)\ =? GMAT Problem Solving
• The population of the bacteria colony doubles every day. If it was started 9 days ago with 2 bacteria and each bacteria lives for 12 days, how large is the colony today? GMAT Problem Solving
• If t/u= x/y and t/y=u/x where t, u, x, and y are non-zero integers, which of the following is true? GMAT Problem Solving
• A farm has chickens, cows and sheep GMAT Problem Solving
• In how many different ways can a group of 8 people be divided into 4 teams of 2 people each? GMAT Problem Solving
• If 4 people are selected from a group of 6 married couples, what is the probability that none of them would be married to each other? GMAT Problem Solving
• If the equation |x|+|y|= 5 encloses a certain region on the graph, what is the area of that region? 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
• (15^11 - 15^10)/14 =? 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
• If,P^2-QR=10,Q^+PR=10,R^2+PQ=10 and R≠QR≠Q, what is the value of P^2+Q^2+R^2? GMAT Problem Solving
• If y (u-c) = 0 and j (u-k) = 0, which of the following must be true, assuming c < kc < k? GMAT Problem Solving
• If 2^98= 256L+N, where L and N are integers and 0≤N≤4, what is the value of N? GMAT Problem Solving
• If m, p, and t are distinct positive prime numbers, then (m^3)(p)(t) has how many different positive factors greater than 1? GMAT Problem Solving
• How many 5-letter words can be formed using the letters of the English alphabet that contain 2 different vowels and 3 different consonants? GMAT Problem Solving
• If a+b+c = 0 and a^3+b^3+c^3 = 216, what is the value of a∗b∗c ? GMAT Problem Solving
• If a polygon has 44 diagonals, then how many sides are there in the polygon? GMAT Problem Solving
• If (a1 + a2 + a3 + .... +an) = 3(2n+1 - 2), for every n≥1, then a11 equals GMAT Problem Solving
• A chord of a circle is equal to its radius GMAT Problem Solving
• A clock loses a minute every three hours for 4 days and gains 1% in the subsequent 6 days GMAT Problem Solving
• A Container in the Shape of a Right Circular Cylinder is 1/2 GMAT Problem Solving GMAT Problem Solving
• How many multiples of 7 are there between 21 and 343, exclusive? GMAT Problem Solving
• How many odd factors does 210 have? GMAT Problem Solving
• How many three-digit integers are not divisible by 3? GMAT Problem Solving
• How many three-digit numbers are there such that all three digits are different and the first digit is not zero? GMAT Problem Solving
• There was a series of two successive discounts of y% on the price of Laptop GMAT Problem Solving
• The product of two negative numbers is 160 GMAT Problem Solving
• In an increasing sequence of 10 consecutive integers, the sum of the first 5 integers is 560 GMAT Problem Solving
• In a battle, 70% of the combatants lost one eye, 80% an ear, 75% an arm, 85% a leg, x% lost all the four limbs. What is the minimum value of x? GMAT Problem Solving
• A librarian has a set of ten books, including four different books about Abraham Lincoln GMAT Problem Solving
• A "standard" deck of playing cards consists of 52 cards in each of the 4 suits of Spades, Hearts, Diamonds, and Clubs GMAT Problem Solving GMAT Problem Solving
• If the sum of the lengths of the edges of a cube is 60 GMAT Problem Solving
• How many even divisors of 1600 are not multiples of 16? GMAT Problem Solving
• How many 5 digit (digit = 0 - 9) zip codes can exist in which at least one digit is repeated ? GMAT Problem Solving
• How Much is the Greatest of Five Consecutive Even Integers Greater than the Smallest? GMAT Problem Solving
• Is Square Root = Always Positive? GMAT Problem Solving
• Following equations has a solution in common with x^2 - 2 GMAT Problem Solving
• What is the units digit of the product (32^28) (33^47) (37^19)? Problem Solving
• The least number of digits (including repetitions) needed to express 10^100 in decimal notation GMAT Problem Solving
• The Largest 3 Digit Number to Have an Odd Number of Factors GMAT Problem Solving
• If 100,000 microns = 1 decimeter, and 1,000,000,000 angstroms = 1 decimeter, how many angstroms equal 1 micron? GMAT Problem Solving
• Greg Assembles Units of a Certain Product at a Factory. GMAT Problem Solving
• A Scientific Research Study Examined a Large Number of Young Foxes, that is, Foxes Between 1 Year and 2 Years Old GMAT Problem Solving
• The Smallest of Six Consecutive Odd Integers Whose Average (arithmetic mean) is x + 2 GMAT Problem Solving
• The Greatest 6-Digit Number When Divided by 6, 7 ,8 , 9, and 10 Leaves a Remainder of 4, 5, 6, 7, and 8 Respectively GMAT Problem Solving