Question

The number of ways to fill each of the four cells of the table with a distinct natural number such that the sum of the numbers is $10$ and the sums of the numbers placed diagonally are equal is

• A. $4$
• B. $8$
• C. $24$
• D. $6$

Answer 1

The correct option is B $8$

The natural numbers are $1,2,3,4$. Clearly, in one diagonal we have to place $1,4$ and in the other $2,3$.
The number of ways in (i) is $2!\times 2!=4$.
The number of ways in (ii) is $2!\times 2!=4$.
Therefore, the total number of ways is $8$.