GMAT® Math Practice - Tossing coins

Concept: Tossing coins simultaneously.

This GMAT Math practice question is a Permutation and Combination problem solving question and the concept tested is finding the outcomes when a set of coins are tossed simultaneously.

Question: Ten coins are tossed simultaneously. In how many of the outcomes will the third coin turn up a head?

  1. 210
  2. 29
  3. 3 * 28
  4. 3 * 29
  5. None of these

Video Explanation

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Explanatory Answer

When a coin is tossed once, there are two outcomes. It can turn up a head or a tail.
When 10 coins are tossed simultaneously, the total number of outcomes = 210

Out of these, if the third coin has to turn up a head, then the number of possibilities for the third coin is only 1 as the outcome is fixed as head.

We need to find out what happens to the remaining 9 coins?
The remaining 9 coins can turn up either a head or a tail. Each of the 9 coins has 2 possibilities.
Number of outcomes for the remaining 9 coins = 29

∴ the number of outcomes in which the 3rd coin turns a head = 1 * 29 = 29.

Choice D is the correct answer.

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