Maths-
General
Easy

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-

  1. 8
  2. 4!    
  3. 24    
  4. None of these    

Hint:

The number of ways to fill each of the four cells of the table with a distinct natural number = Total ways of filling (x, b) cross times total ways of of filling (y, a)

The correct answer is: 8



    According to question and xyab=10
    So b and y5
    Given: all number should be different and two pairs whose sum is 5.
    We have 2 pair of natural number that is (1,4),(2,3) whose sum is 5Error converting from MathML to accessible text.
    We can choose 1 pair among 2 of them for (xb) by 2! ways and they can rearranged in 2ways. 
    So total ways for (xb) will be 2!×2!
    Remaining one pair will be for (ay) and they can be arranged by 2! ways.  
    So total ways for (ya will be 2!.

    Combining both situation together we get 2× 2× 2!8

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