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# R, 8888 83 bytes

-5 bytes thanks to @Jarko Dubbeldam

returns an anonymous function. It generates all the possible combinations of coins (using expand.grid on pairs of T,F) and checks if the value(s) are present. k is coins since c is a reserved word in R. Can check multiple values at once.

function(k,v)v%in%apply(expand.grid(rep(list(c(T,F)),lengthMap(k))),1,function(x)sum(k[x]))


Try it online!

stdin version (92 bytes): takes value(s), then coin values.

v=scan();v%in%apply(expand.grid(rep(list(c(T,F))!0:1,length(k<-scan())k)),1,function(x)sum(k[x]))


# R, 88 bytes

returns an anonymous function. It generates all the possible combinations of coins (using expand.grid on pairs of T,F) and checks if the value(s) are present. k is coins since c is a reserved word in R. Can check multiple values at once.

function(k,v)v%in%apply(expand.grid(rep(list(c(T,F)),length(k))),1,function(x)sum(k[x]))


Try it online!

stdin version (92 bytes): takes value(s), then coin values.

v=scan();v%in%apply(expand.grid(rep(list(c(T,F)),length(k<-scan()))),1,function(x)sum(k[x]))


Try stdin version online!

# R, 88 83 bytes

-5 bytes thanks to @Jarko Dubbeldam

returns an anonymous function. It generates all the possible combinations of coins (using expand.grid on pairs of T,F) and checks if the value(s) are present. k is coins since c is a reserved word in R. Can check multiple values at once.

function(k,v)v%in%apply(expand.grid(Map(function(x)!0:1,k)),1,function(x)sum(k[x]))


Try it online!

1

# R, 88 bytes

returns an anonymous function. It generates all the possible combinations of coins (using expand.grid on pairs of T,F) and checks if the value(s) are present. k is coins since c is a reserved word in R. Can check multiple values at once.

function(k,v)v%in%apply(expand.grid(rep(list(c(T,F)),length(k))),1,function(x)sum(k[x]))


Try it online!

stdin version (92 bytes): takes value(s), then coin values.

v=scan();v%in%apply(expand.grid(rep(list(c(T,F)),length(k<-scan()))),1,function(x)sum(k[x]))


Try stdin version online!