All the letters of the word "GTWENTY" are written in all possible ways with or without mea…

Question

All the letters of the word "GTWENTY" are written in all possible ways with or without meaning and these words are written as in a dictionary. The serial number of the word "GTWENTY" is \_\_\_\_\_\_\_\_\_.

Answer: 553

Accepted Answer

Letters of GTWENTY in alphabetical order: E, G, N, T, T, W, Y (with T repeated twice).

Words starting with E: $\dfrac{6!}{2!} = 360$

Words starting with GE: $\dfrac{5!}{2!}\times... $ --- fixing G, remaining letters E,N,T,T,W,Y arranged, then within G-words, those starting with GE: $\dfrac{5!}{2!}=60$

Words starting with GN: $60$

Words starting with GTE: $4!=24$

Words starting with GTN: $24$

Words starting with GTT: $24$

Words starting with GTWENTY itself: $1$

$$\text{Total} = 360+60+60+24+24+24+1 = 553$$

Solutions · 1