A professor writes 40 discrete mathematics true/false questions. Of the statements in these questions, 17 are true. If the order matters here , how many different answer keys are possible?
I know that if order does not matters, then it is simply a combination problem of choosing 17 out of 40 elements.
But now order matters here, So I answered it as C(40,17) * 2^40.
Am I right here ?
This question is same as bit string question in which Total length of bit string is 40. Of which 17 are 1's and 23 are 0's.
So, by using permutations, we are having total 40 elements in which 17 are of one kind and 23 are of other kind.
So, the whole problem reduces to 40! / (17! * 23!) = C(40,17)