Question: 2017 Winter Midterm - 8
Each student has a student number which is a string of five digits, in which no digit occurs more
than once. Thus, 94631 is a valid student number, whereas 94641 is not valid.
What is the minimum number of students such that we can guarantee that at least two of them have the same student number?
What is the minimum number of students such that we can guarantee that at least two of them have the same student number?
(a)
$1 + \frac{5!}{10!}$
(b)
$1 + 5^{10}$
(c)
$1 + \frac{10!}{5!}$
(d)
$1 + 10^{5}$