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How many of the following functions are Binomial probability mass functions?

i. $p(x)={30 \choose x} p^x(1-p)^{15-x}$ for $x=0,1,2,\ldots,15$

ii. $p(x)=p^x(1-p)^{1-x}$ for $x=0,1$

iii. $p(x)={10 \choose 5} p^5(1-p)^{10-5}$

iv. $p(x)={5 \choose x}p^x(1-p)^{5-x}$ for $0\leq x\leq5$

v. $p(x)=\dfrac{2!}{x!(2-x)!}p^x(1-p)^{2-x}$ for $x=0,1,2$

A

$0$

B

$1$

C

$2$

D

$3$

E

$4$

F

$5$

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