Question

A nursery teacher has 5 pencil boxes to give out to her five students. Determine the probability that at least one student gets their name tag?

(a) \(\frac{19}{30}\)

(b) \(\frac{26}{47}\)

(c) \(\frac{123}{537}\)

(d) \(\frac{12}{79}\)

I had been asked this question in an interview for job.

I would like to ask this question from Counting in division Counting of Discrete Mathematics

Answer 1

Right option is (a) \(\frac{19}{30}\)

Best explanation: There are 5!= 120 ways to give out the pencil boxes. By using complementary probability, the number of ways where nobody gets their pencil boxes is

5!(\(\frac{1}{0!} – \frac{1}{1!} + … – \frac{1}{5!}\))

= 44. Hence, the required probability is  \(\frac{120 – 44}{120} = \frac{19}{30}\).