# GMAT Quant Questions | Permutation Q15

#### Outcomes of Tossing coins | Permutation Combination

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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### 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 nCr
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

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