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The number of ways to fill each of the four cells of the table

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:

4

8

24

6

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Elijah Discussed

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:

12 mins ago

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12 mins ago

Text solutionVerified

According to question

x + b = a + y

and

x + y + a + b = 10

x + b = 5

and

a + y = 5

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

5

We can choose

1

pair among

2

of them for

(x, b)

2!

ways and they can rearranged in

2!

ways.

So total ways for

(x, b)

will be

2! \times 2!

Remaining one pair will be for

(a, y)

and they can be arranged by

2!

ways.

So total ways for

(y, a)

will be

2! .

Combining both situation together we get

2! \times 2! \times 2! = 8

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Question Text	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:
Answer Type	Text solution:1
Upvotes	153

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:

Text solutionVerified

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