Question: 2014 Fall Midterm - 1

Author: Michiel Smid

Let $n \geq 2$ be an integer. How many bitstrings of length $n$ are there that contain at least two 1s?

a) ${n \choose 2} \cdot 2^{n-2}$

b) $n \cdot 2^{n-1}$

c) $2^{n} - 1 - n$

d) $2^{n} - n$

Let $n \geq 2$ be an integer. How many bitstrings of length $n$ are there that contain at least two 1s?

(a)

$2^{n} - 1 - n$

(b)

$n \cdot 2^{n-1}$

(c)

$2^{n} - n$

(d)

${n \choose 2} \cdot 2^{n-2}$