Question

In a certain strange language, words are written with letters from the following six-letter alphabet: $A,G,K,N,R,U$. Each word consists of six letters and none of the letters repeat. Each combination of these six letters is a word in this language. The word $"KANGUR"$ remains in the dictionary at.

• A. ${248}^{th}$
• B. ${247}^{th}$
• C. ${246}^{th}$
• D. ${253}^{rd}$

Answer 1

The correct option is A ${248}^{th}$

$A,G,K,N,R,U$

By dictionary $\to$ Alphabetical

$\underset{–}{A}\underset{–}{}\underset{–}{}\underset{–}{}\underset{–}{}\underset{–}{}$

${}^5{C}_1{\times }^4{C}_1{\times }^3{C}_1{\times }^2{C}_1{\times }^1{C}_1=5!$

Similarly $\underset{–}{G}\underset{–}{}\underset{–}{}\underset{–}{}\underset{–}{}\underset{–}{}\to 5!$

$\underset{–}{K}\underset{–}{A}\underset{–}{G}\underset{–}{}\underset{–}{}\underset{–}{}$

${}^3{C}_1{\times }^2{C}_1{\times }^1{C}_1=3!$

$\underset{–}{K}\underset{–}{A}\underset{–}{N}\underset{–}{G}\underset{–}{}\underset{–}{}RU$ or $UR\to 2!$

Total $=5!+5!+3!+2!$

$={248}^{th}$ word