We give a complete classification of right coideal subalgebras that contain
all group-like elements for the quantum group $U_q^+(\frak{so}_{2n+1}),$
provided that $q$ is not a root of 1. If $q$ has a finite multiplicative order
$t>4,$ this classification remains valid for homogeneous right coideal
subalgebras of the small Lusztig quantum group $u_q^+(\frak{so}_{2n+1}).$ As a
consequence, we determine that the total number of right coideal subalgebras
that contain the coradical equals $(2n)!!,$ the order of the Weyl group defined
by the root system of type $B_n.$