Question

Determine the number of ways In a single competition a singing couple from 5 boys and 5 girls can be formed so that no girl can sing a song with their respective boy?

(a) 123

(b) 44

(c) 320

(d) 21

The question was asked in an interview for internship.

Question is from Counting topic in section Counting of Discrete Mathematics

Answer 1

Correct answer is (b) 44

The best I can explain: This is a case of derangement of 5 boys and 5 girls. The required number of ways can be described as D = 5! (1 – \(\frac{1}{1!} + \frac{1}{2!} – \frac{1}{3!} + \frac{1}{4!} – \frac{1}{5!}) = 120(\frac{11}{30})\) = 44 ways.