Let x be the fourth digit of your student ID (without leading zero), y be the sixth

digit of your student ID. The value N used in this task is given by 5x + 6y + 15.

For the below tasks, you need to show your working by providing formula used, and/or

short explanation. Also give the numerical final answer (e.g. 1024 instead of 210).

Assume your x=3 and y=4.

(a) Assuming that we have 230 students enrolled in this subject, and all student

numbers are randomly generated. What's the probability that at least one of

your classmate shares the same N with you? Your result should be rounded to

three digits after the decimal point.

(b) How many ways to place N different balls into five different bins?

(c) How many ways to place N identical balls into five different bins, so that all bins

are non-empty?

(d) How many ways to place N identical balls into five different bins?

(e) How many ways to place N identical balls into five identical bins, so that at most

two bins are non-empty?