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In a community, 8 people are applying The community is either 4 5, 6 members in length. Special people Kashish and George are applying. Find the probability George makes it to the community.

The total possibilities, denominator is:

$$\binom{8}{6} + \binom{8}{5} + \binom{8}{4}$$

We would like George there, so there are $1 + 1 + 1$ ways in each scenario.

So what would the total Probability be?

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    You have to specify the selection process in more detail. Do you first choose a number of members randomly from $4,5,6$ and then choose the members, do you make a list of all the acceptable committees and choose one, or something else? As there are many more committees with $4$ members and they are less likely to include George than committees with more members it will change the probability. Often the hard part in questions like this is making it precise enough to do the computation. – 2017-01-23
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    Are you mixing up the words "community" and committee" ? – 2017-01-23

1 Answers 1

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As has been pointed out, your question isn't too clear.

Assuming that we are equally likely to form a committee of $4,5,\;or\;6$ from $8$ applicants,

George has to be on the committee, so the balance members need to be chosen from $7$ others.

P(George is on the committee) = $\dfrac{\dbinom73 + \dbinom74 + \dbinom75}{\dbinom84 + \dbinom85 + \dbinom86}$