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

A nursery teacher has 5 pencil boxes to give out to her five students.

1.	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» 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\(\frac{120 – 44}{120} = \frac{19}{30}\).

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