Select $n$ from $2n$

Probability Level 3

In how many ways can we select $n$ objects from a collection of size $2n$ that consists of $n$ distinct and $n$ identical objects?

2^n

\frac{(2n)!}{n!}

n!

\binom{2n}{n}

1 solution

Brian Lie
Mar 17, 2021

We can select $k$ objects from the collection of $n$ distinct objects and $n-k$ objects from the collection of $n$ identical objects in $\binom{n}{k}$ ways, making the answer $\sum_{k=0}^n\binom{n}{k}=2^n.$

Select n n n from 2 n 2n 2 n

1 solution

0 pending reports

Select $n$ from $2n$