A professor writes 40 discrete mathematics true/false questions. Of the statements in these questions, 17 are true

BolkowN

BolkowN

Answered question

2021-09-08

A professor writes 40 discrete mathematics true/false questions. Of the statements in these questions, 17 are true. If the questions can be positioned in any order, how many different answer keys are possible?

Answer & Explanation

Neelam Wainwright

Neelam Wainwright

Skilled2021-09-09Added 102 answers

Definition permutation: P(n,r)=n!(nr)! Definition combination: C(n,r)=(nr)=n!r!(nr)!
nn(n1)21 Solution The order of the questions does not matter (because all selected auestions will just true), thus we then need to use the definition of combination. There are 40 questions of which 17 are true. n=40
r=17
Evaluate the definition of a combination: C(40,17)=40!17!(4017)!=40!17!23!=88,732,378,800 Answer: 88,732,378,80 answer keys

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