Ten coins are tossed simultaneously. In how many of the outcomes will the third coin turn up a head?  Choices:
A) 2(10)
B) 2(9)
C) 3 * 2(8)
D) 3 * 2(9)
E) None of these
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 = 2(9)   ∴ the number of outcomes in which the 3rd coin turns a head = 1 * 2(9) = 2(9).   Choice 3 * 2(9)
<result>D</result>
Ten coins are tossed simultaneously. In how many of the outcomes will the third coin turn up a head?