Problem #4

Probability Level 3

Let $S$ be a 10-element set.

John randomly picks a 5-element subset $A$ from $S$ . Then Joel picks a 3-element subset $B$ from $S$ .

What is the probability that $B$ is a subset of $A$ ? If the answer is $\frac {m}{n}$ where $m, n$ are coprime positive integers find $m+n$ .

This problem is part of the set Easy Problems

The answer is 13.

1 solution

Jared Low
Nov 30, 2014

There are ${10 \choose 5}=252$ possibilities for 5-element subset $A$ of $S$ , ${10 \choose 3}=120$ possibilities for 3-elements subset $B$ of $S$ and ${5 \choose 3}=10$ possibilities for a 3-element subset of $A$ .

The probability that subset $B$ is a subset of $A$ is thus $\frac{10}{120}=\frac{1}{12}=\frac{m}{n}$ .

We finally have $m+n=\boxed{13}$

Problem #4

The answer is 13.

1 solution

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