A group of 48 friends meets for lunch. They greet each other by exchanging fist bumps. How many fist bumps are exchanged if each
friend must bump with each of the 47 others?
2 answers:
2256 fist bumps. 47 fist bumps x 48 friends is 2256 fist bumps.
Answer:
The correct answer is 1128 fist bumps exchanged.
Step-by-step explanation:
Each friend exchanges 47 fist bumps, one for each friend on the group.
If the group is made up of 48 friends, and each exchange is done by 2 friends, you have to divide by 2 each interaction:
(48 friends * 47 first bumps) / 2 friends = (2256 friends per first bumps exchanged) / 2 friends = 1128 fist bumps exchanged.
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1st) the common ratio is (1/4 : 1/2 ) = 1/2, so r =1/2
2nd) the sum of a GP is:
S= a(1-rⁿ)/(1-r)
S=(1/2).[1-(1/2)⁴]/(1-1/2) = 15/16
