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?

- 2
^{10} - 2
^{9} - 3 × 2
^{8} - 3 × 2
^{9} - None of these

@ INR

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 = 2^{10}

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 = 2^{9}

∴ the number of outcomes in which the 3rd coin turns a head = 1 × 2^{9} = 2^{9}.

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