We use three coins (quarter, nickel, dime) each are flipped only once. We get 8 possible outcomes (or four outcomes as an alternative).
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There are two outcomes for each coin and three coins; 2 x 2 x 2 = 23 = 8 outcomes.
Two possible outcomes for each flip. 2,048 possible histories of 11 flips.
In three flips of a fair coin, there are a total of 8 possible outcomes: T, T, T; T, T, H; T, H, T; T, H, H; H, H, H; H, H, T; H, T, H; H, T, T Of the possible outcomes, four of them (half) contain at least two heads, as can be seen by inspection. Note: In flipping a coin, there are two possible outcomes at each flipping event. The number of possible outcomes expands as a function of the number of times the coin is flipped. One flip, two possible outcomes. Two flips, four possible outcomes. Three flips, eight possible outcomes. Four flips, sixteen possible outcomes. It appears that the number of possible outcomes is a power of the number of possible outcomes, which is two. 21 = 2, 22 = 4, 23 = 8, 24 = 16, .... Looks like a pattern developing there. Welcome to this variant of permutations.
When you toss a coin four times, each toss has 2 possible outcomes: heads or tails. To find the total number of outcomes, you multiply the number of outcomes for each toss together. In this case, it would be 2 x 2 x 2 x 2 = 16 possible outcomes.
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