1. Tardigrade
  2. Question
  3. Mathematics
  4. Number of ways in which the letters of the word NATION can be filled in the given figure such that no row remains empty and each box contain not more than one letter is (K)6!. The value of K equals

Question Error Report

Thank you for reporting, we will resolve it shortly

Back to Question

Q. Number of ways in which the letters of the word "NATION" can be filled in the given figure such that no row remains empty and each box contain not more than one letter is $(K)6!$. The value of K equalsMathematics Question Image

Permutations and Combinations

Solution:

Any six blocks can be selected for 6 letters in ${ }^8 C _6$ but this includes, when top 2 or middle two are not selected
$\therefore $ effective number of ways $={ }^8 C _6-2={ }^8 C _2-2=26$
six letters of "NATION" can be arranged in $\frac{6 !}{2}$ ways
Total ways $=26 \cdot \frac{6 !}{2}=13 \cdot 6 ! \Rightarrow K=13$.