We can order in terms of the number of S's picked.
If no S's are picked the only way to pick four letters in POEE. There are
\[\frac{4!}{2!}=12\]
arrangements.If one S is picked then we could pick
SOEP which can be arranged in
\[4!=24\]
ways.SOEE which can be arranged in
\[\frac{4!}{2!} = 12\]
ways.SPEE which can be arranged in
\[\frac{4!}{2!} = 12\]
ways.If two S's are picked we could pick
SSOE which can be arranged in
\[\frac{4!}{2!} = 12\]
ways.SSPE which can be arranged in
\[\frac{4!}{2!} = 12\]
ways.SSPO which can be arranged in
\[\frac{4!}{2!} = 12\]
ways.SSEE which can be arranged in
\[\frac{4!}{2!2!} = 6\]
ways.If three S's are picked then we could pick
SSSE which can be arranged in
\[\frac{4!}{3!} = 4\]
ways.SSSO which can be arranged in
\[\frac{4!}{3!} = 4\]
ways.SSSP which can be arranged in
\[\frac{4!}{3!} = 4\]
ways.If four S's are picked there is only one arrangement.
Adding up all the possibilities gives
\[12+24+12+12+12+12+12+6+4+4+4+1=115\]
.