JEE Main · 2016 · 03 Apr 2016 · Offline · Permutations and Combinations

The letters of SMALL are A, L, L, M, S. Count the dictionary blocks before it: words starting with A arrange the remaining L, L, M, S in $\frac{4!}{2!}=12$ ways; those starting with L arrange A, L, M, S in $4!=24$ ways; those starting with M arrange A, L, L, S in $\frac{4!}{2!}=12$ ways, giving 48 so far. Then words starting SA arrange L, L, M in $\frac{3!}{2!}=3$ ways, and words starting SL arrange A, L, M in $3!=6$ ways, adding 9 to reach 57. The next word is SMALL itself, so its position is the 58th.