Question
If all the words (with or without meaning) having five letters, formed using the letters of the word SMALL and arranged as in a dictionary; then the position of the word SMALL is:
A.
$${52^{nd}}$$
B.
$${58^{th}}$$
C.
$${46^{th}}$$
D.
$${59^{th}}$$
Answer :
$${58^{th}}$$
Solution :
ALLMS
No. of words starting with
$$\eqalign{
& {\text{A}}\,\,:\,\,\underline {\text{A}} \,\,\underline {} \,\,\underline {} \,\,\underline {} \,\,\underline {} \,\,\frac{{4!}}{{2!}} = 12 \cr
& {\text{L}}\,\,:\,\,\underline {\text{L}} \,\,\underline {} \,\,\underline {} \,\,\underline {} \,\,\underline {} \,\,4! = 24 \cr
& {\text{M}}\,\,:\,\,\underline {\text{M}} \,\,\underline {} \,\,\underline {} \,\,\underline {} \,\,\underline {} \,\,\frac{{4!}}{{2!}} = 12 \cr
& {\text{S}}\,\,:\,\,\underline {\text{S}} \,\,\underline {\text{A}} \,\,\underline {} \,\,\underline {} \,\,\underline {} \,\,\frac{{3!}}{{2!}} = 3 \cr
& \,\,\,\,\,\,:\,\,\underline {\text{S}} \,\,\underline {\text{L}} \,\,\underline {} \,\,\underline {} \,\,\underline {} \,\,3! = 6 \cr
& {\text{SMALL}}\,\,\,®\,\,\,{58^{th}}\,\,{\text{word}} \cr} $$