Q. The number of four-letter words that can be formed (the words need not be meaningful) using the letters of the word MEDITERRANEAN such that the first letter is E and the last letter is R, is
A) $\frac{11!}{2!2!2!}$
B) 59
C) 56
D) $\frac{11!}{3!2!2!}$
Explanation
(b)
Word MEDITERRANEAN has 2A, 3E, 1D, 1I, 1M, 2N, 2R, 1T
In out of four letters E and R is fixed and rest of the two letters can be chosen in following ways
Case I Both letter are of same kind $ie$, $\ ^{3}C_{2}$ ways, therefore number of words $= \ ^{3}C_{2} \times \frac{2!}{2!} = 3$
Case II Both letters are of different kinds $ie$, $\ ^{8}C_{2}$ ways, therefore number of words$= \ ^{8}C_{2} \times 2! = 56$
Hence, total number of words=56+3=59
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.