How many ways are there to answer a 10-question true/false test, where at least 3 of the questions have been answered with a false?
I got 14 but that is incorrect.
+2539 Solution:
There are (10C3) 120 ways to choose where to place the three false responses. This leaves (27) 128 ways to respond to the remaining questions with true or false.
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How many ways are there to answer a 10-question true/false test, where at least 3 of the questions have been answered with a false?
There are (10C3) 120 ways to choose where to place the three false responses. This leaves (27) 128 ways to respond to the remaining questions with true or false.
(10C3) = 120 * 128 15360
This continues with
(10C4) = 210 * 64 13440
(10C5) = 252 * 32 8064
(10C6) = 210 * 16 3360
(10C7) = 120 * 8 960
(10C8) = 45 * 4 180
(10C9) = 10 * 2 20
(10C10) = 1 * 1 1
Sums 968 256 35185
Analysis: There are 35185 ways to answer 10 question T/F with 3 or more pre-answered questions. Total includes multiple redundancies. At least 64 permutations will not exist in the totals.
GA
Here's the answer: we can find the total number of combinations (without any restrictions) and then subtract the number of combinations that have less than 3 "false" answers.
the number of combinations without any restrictions is 210 (because there are 10 questions and each question can be answered with "true" or "false", meaning that there are 2 possible answers for each question).
the number of combinations with less that 3 questions answered with "false" is:
(number of combinations with exactly 2 questions answered with "false")+(number of combinations with exactly 1 question answered with "false")+(number of combinations with no questions answered with "false")= (10 choose 2)+(10 choose 1)+10 choose 0) (because we have to choose the questions that will be answered with "false")
(10 choose 2)+(10 choose 1)+10 choose 0)=56, so all we have to do to find the number of combinations that follow the restriction is to subtract 56 from 210=1024: 1024-56=968. and that's the answer to the question.
Ginger has a wrong answer. That doesn’t happen very often. I wonder how she will respond.
Ginger says I’m an armchair mathematician. This is like an armchair quarterback except for mathematics. I’m not very good at solving math problems but I usually recognize a correct answer and a well-presented solution when I see it. Likewise, I usually recognize an incorrect answer and a poorly presented solution when I see it.
I didn’t notice Ginger’s answer was wrong until I saw this one. But I did notice this one is wrong. It’s not just wrong it’s fu*ked up!
