GMAT Quant Practice Questions

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

Question 7: 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

Explanatory Answer | GMAT Tossing Coins Q7

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 B is the correct answer.