hSuppose you flip a coin and keep a record of the results. In how many ways could you obtain at least one head if you flip the coin five times?

Question

how would i solve this ?

Answer 1

ways to get at least 1 head = total number of ways minus the ways to get zero heads in 5 flips.

2^5 - 1 = 32-1 = 31 ways to get at least 1 head in 5 flips

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5 ways to get exactly 1 head

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10 ways to get exactly 2 heads

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10 ways to get exactly 3 head

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5 ways to get exactly 4 head

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1 way to get exactly 5 heads

5+10+10+5+ 1= 31 ways to not get 0 heads & get exactly 1 head

or calculate it with Combinations, nCr = n!/(n-r)!r!

5C0 = 5!/(5-0)!0! = 5!/5! = 1

5C1 = 5!/4!1! = 5

5C2 = 5!/3!2! = 5(4)/2 = 10

5C3 = 5!/2!3! = 10

5C4 = 5!/1!4! = 5

5C5 = 5!/5!0! = 1

1+5+10+10+5+ 1 -1 = 31 ways to get at least 1 head