# HW01.pdf - MATH-UA.0233 Dr M Nitzschner Theory of...

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MATH-UA.0233 Theory of Probability Fall 2021 Dr. M. Nitzschner Problem Set 1 Submission: Thursday, 09/16/2021, until 1 PM, to be uploaded on the NYU Brightspace course homepage. 1. Elementary combinatorics [4 Points] Use the results on elementary combinatorics seen in the lecture. Explain your reasoning. (a) How many possibilities are there to distribute 10 indistinguishable coins to 4 di erent persons? (b) Assume you have 7 colors to mark 4 di erent courses you have taken this term in your notes. How many possibilities to choose these colors are there, if every subject has its distinct color. (c) There are 5 lamps in a room, that can be turned on or o independently from each other. How many possibilities are there for the con guration of lights? (d) In a lottery, 6 out of 49 numbers are chosen at once. How many possibilities are there to guess exactly 3 out of these numbers correctly? Hence, calculate the probability to guess 3 out of 6 numbers correctly in this type of lottery.