If all the letters of the word REPEAT are permuted in all possible ways and if the six letter permutations thus formed are arranged in the dictionary order, then the rank of the word REPEAT is

On arranging the letters of world REPEAT in alphabetic order, we get AEEPRT. Now, the number of words starts with \(R\). \(=\frac{5 !}{2 !}=60\) The number of words starts with \(E\) \(=5 !=120\) The number words starts with \(P\) \(=\frac{5 !}{2 !}=60\) The number of words starts with \(R A\) \(=\frac{4 !}{2 !}=12\) The number of words starts with REA \(=3 !=6\) The number of words starts with REE \(=3 !=6\) The number of words starts with REPA \(=2 !=2\) The number of words starts with REPEAT \(=1 !=1\) Now, the rank of word REPEAT is \(=60+120+60+12+6+6+2+1=267\) Hence, option (b) is correct.