A Group of Six Friends (A, B, C, D, E and F) Plans on taking a Ride GMAT Problem Solving

Question:  A group of six friends (A, B, C, D, E, and F) plans on taking a ride in a boat that only has room for three people. The three friends draw to see who will go. The probability of A being chosen, but B not, is:

(A) 6/15
(B) 3/10
(C) 4/6
(D) ½
(E) 4/5

“A group of six friends (A, B, C, D, E and F) plans on taking a ride in a boat that only has room for three people" - is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been borrowed from the book “GMAT Official Guide Quantitative Review”.

To understand GMAT Problem Solving questions, applicants must possess fundamental qualitative skills. Quant tests a candidate's aptitude in reasoning and mathematics. The GMAT Quantitative test's problem-solving phase consists of a question and a list of possible responses. By using mathematics to answer the question, the candidate must select the appropriate response. The problem-solving section of the GMAT Quant topic is made up of very complicated math problems that must be solved by using the right math facts.

Answer: B
Solution and Explanation:
Approach Solution 1:

The question asks us to determine the probability of A being chosen but not B. It is given that there are six friends named A, B, C, D, E, F. Three of them are selected to take a ride on the boat.

To solve the problem, the candidate must recall the following permutation and combination formulas.

nPr = n! / (n-r)! permutation of n items taken r at a time
Combination of n things, r at a time: nCr = n! / ((n-r)!)! * r!)
where x! = x*(x-1)*(x-2)*......(3).(2).(1)

Let us explore the situation in which A is selected but B is not.

A was selected, but B was not; now we need to select two persons from the group of four that is left; there are a total of four times two, which is equal to six different possibilities.
Total ways = 6C3 = 20
Probability = 6/20 = 3/10

B is the correct answer.

Correct Answer: B

Approach Solution 2:

The question asks us to determine the probability of A being chosen but not B. It is given that there are six friends named A, B, C, D, E, and F. Three of them are selected to take a ride on the boat.
Let us consider a case when A is chosen and B is not.
Now we have remaining 4 people who are to be selected and 2 of them will be selected in the crew
Now first person can be selected in 3 ways
And second person can be selected in 2 ways
Total 3 people can be selected including A and not B : 2 x 3 = 6 ways

Now total number of ways of selecting 3 people among 6 people is:
1st person can be selected from 6 people in 6 ways
2nd person can be selected in 5 ways
3rd can be selected in 4 ways
Total ways of selecting 3 people = 6 x 5 x 4 = 120
They can be arranged in 3! ways , so total unique ways = 120/ 3! = 20
Probability = 6/20 = 3 / 10
B is the correct answer.

Correct Answer: B

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