How do you calculate the total number of possibilities for several events to occur?
The fundamental counting principle: If there are m ways one event can happen and n ways a second event can happen, then there are m x n ways for the 2 events to happen. For example, with 5 shirts and 7 pairs of pants to choose from, you can have 5 x 7 = 35 different outfits.
To calculate the total number of possibilities for several events to occur, you need to use the multiplication principle of counting.
The multiplication principle states that if there are two events A and B, where event A can happen in m ways and, for each of these m ways, event B can happen in n ways, then the total number of possibilities for the two events to occur in sequence is m x n.
If there are more than two events, you just need to keep multiplying their respective number of possibilities to find the total number of possibilities for all events to occur.
For example, consider an experiment in which a participant rolls a fair six-sided die and then flips a fair coin. To find the total number of possibilities for this experiment, we multiply the number of possibilities for rolling the die (6) by the number of possibilities for flipping the coin (2):
Total number of possibilities = 6 x 2 = 12
So, there are 12 possible outcomes for this experiment.
If we add another event, say the participant selects a card from a shuffled deck of cards (52 cards), we can find the total number of possibilities for all three events to occur using the same multiplication principle:
Total number of possibilities = 6 x 2 x 52 = 624
So, there are 624 possible outcomes for the three events to occur in sequence.
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