In the first round, one person chooses 3 people. In round 2, those 3 people choose 3 people each. Keeping with the pattern, how many people get chosen in round 6?

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Answer 1 · 2017-02-06T10:29:52

#3^6=729#

We have six Rounds of choosing people:

R1: 3 are chosen

R2: 3 choose 3, or #3xx3=3^2=9# are chosen

R3: 9 choose 3, or #9xx3=3^2xx3=3^3=27# are chosen

and so on.

And so we can conclude that the pattern of the number of people being chosen in any given round is:

#3^R#, where #R="round"#

Therefore, in the 6th round, we'll have:

#3^6=729#