On a quiz show, you can pick two envelopes. One envelope has $1000 in it, one has $500, one has $300, one has $200, one has $50, and one is empty. How many different amounts can be won?
by 
-NUNYA--
ANSWERS: 3
-
See if you can interpret my answer: 00011 00101 00110 01001 01010 01100 10001 10010 10100 11000 This is one (painful) way to solve the problem, but it's really just a simple "n things taken m at a time" problem.
-
There are SIX envelopes to choose from. If all the sums are different, then the answer is "6 choose 2" or 6C2 which is (6*5)/(2*1) = 15 So are they all different? If you pick $50 the result will end $50 so will be different from all other sums without $50. If you pick $1000, there's no other way to make that much, so will be different from all other results not choosing $1000 That leaves $500 $300 and $200 AND ZERO. $500 + $0 = $300 + $200, so one pair of amounts will be duplicated. (EDIT: edited to account for the empty envelope. I and yeroca both appear to have seen five envelopes in the question, not six)
-
Yes, what that other guy said.
yeroco RELATED QUESTIONS
Copyright 2023, Wired Ivy, LLC