Question

Farhan has received 9 gifts from 9 different people. In how many ways can Farhan receives the gifts such that no one gives him real gifts?

(a) 133496

(b) 326654

(c) 218744

(d) 745331

I have been asked this question by my school teacher while I was bunking the class.

Asked question is from Counting topic in division Counting of Discrete Mathematics

Answer 1

Correct choice is (a) 133496

The best explanation: By the derangements formula, the number of possible derangements should be 9!(\(\frac{1}{0!} – \frac{1}{1!} + … – \frac{1}{9!}\)) = 133496. Hence, there are a total of ways to give the gifts to him such that no one distributes the real gifts.