Question: 2013 Fall Midterm - 9
Which of the following is true?
(a)
$\sum_{k=0}^{n} 4^{k}5^{n-k}{{n}\choose{k}} = 20^{n}$
(b)
$\sum_{k=0}^{n} 5^{k}{{n}\choose{k}} = 6^{n}$
(c)
$\sum_{k=0}^{n} 5^{k}{{n}\choose{k}} = 5^{n}$
(d)
$\sum_{k=0}^{n} 4^{n-k}5^{k}{{n}\choose{k}} = 8^{n}$