A coin is tossed three times and the outcomes are recorded. How many possible outcomes are there? How many possible outcomes if the coin is tossed four times? Five times? *n* times?

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#### Solution

Total number of outcomes when a coin is tossed once = 2 (Heads, Tails)

Number of outcomes when the coin is tossed for the second time = 2

∴ Number of outcomes when the coin is tossed thrice = `2xx2xx2=8`

Similarly, the number of outcomes when the coin is tossed four times =`2xx2xx2xx2=16`

Similarly, the number of outcomes when the coin is tossed five times =`2xx2xx2xx2xx2=32`

Similarly, the number of outcomes when the coin is tossed '*n*' times = `2xx2xx.......n`times `= 2^n`

Concept: Concept of Permutations

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