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

Get to Q51 in GMAT Quant


Online GMAT Course
@ INR 3500


Video Explanation


GMAT Live Online Classes


Starts Tue, Aug 17, 2021


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

Choice D is the correct answer.



GMAT Online Course
Try it free!

Register in 2 easy steps and
Start learning in 5 minutes!

★ Sign up

Already have an Account?

★ Login

GMAT Live Online Classes

Next Batch Aug 17, 2021

★ GMAT Live Info

GMAT Coaching in Chennai

Next Batch
after Lockdown

★ GMAT Class Info

GMAT Coaching in Chennai

Sign up for a Free Demo of our GMAT Classes in Chennai

★ Schedule Demo

GMAT Permutation Probability Videos On YouTube


GMAT Sample Questions | Topicwise GMAT Questions


Where is Wizako located?

Wizako - GMAT, GRE, SAT Prep
An Ascent Education Initiative
14B/1 Dr Thirumurthy Nagar 1st Street
Nungambakkam
Chennai 600 034. India

How to reach Wizako?

Phone: (91) 44 4500 8484
Mobile: (91) 95000 48484
WhatsApp: WhatsApp Now
Email: learn@wizako.com
Leave A Message