GMAT Quant Questions | Permutation Q15

This sample GMAT Math question is a coin tossing problem solving question. The concept tested is to find the number of times the coin is tossed after a certain data is given. An interesting permutation question.

Question 15: A fair coin is tossed 'n' times. If the number of outcomes in which two heads will appear is 28, what is the value of 'n'?

1. 14
2. 6
3. 7
4. 8
5. 32

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Video Explanation

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Explanatory Answer | Outcomes of Tossing Coins

Step 1 of solving this GMAT Permutation Question: Understanding the question

The number of outcomes in which 'r' heads will appear in 'n' tosses of a coin is nC_r
So, the number of outcomes in which 2 heads will appear in 'n' tosses is nC₂
nC₂ = \\frac{n(n - 1)}{2})
From question stem, number of outcomes = 28
So, nC₂ = \\frac{n(n-1)}{2}) = 28
n(n - 1) = 56

Step 2 of solving this GMAT Permutation Question: Method 1: Solve the quadratic equation by factorization

n² - n - 56 = 0
n² - 8n + 7n - 56 = 0
(n - 8)(n + 7) = 0
n = 8 or n = -7
Number of tosses cannot be negative. So, n = 8

Step 2 of solving this GMAT Permutation Question: Method 2: Product of two consecutive positive integers (n - 1) and n is 56.

Which two numbers will satisfy this condition?
n = 8 and (n - 1) = 7
So, n = 8

Choice D is the correct answer.