Explanation Given, The arrangement of numbers in each row of Pascal’s triangle is symmetric. The 4s are balanced in the fourth row, the 5s are balanced in the fifth row, and so on. Expressing individual values in Pascal’s triangle as C ( n , r ) , with n and r being integers obeying the relation − 1 < r ≤ n this means that each C ( n , r ) = C ( n , n − r ) . Since, Pascal’s triangle is essentially a table in which the look up binomial coefficients, C ( n , r ) = ( n , r ) From Pascal’s rule it follows that C ( n , r ) = C ( n − 1 , r − 1 ) + C ( n − 1 , r ) . Obviously C ( 0 , r ) = 1 because there is only one way to choose r items from a collection of r items

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Chapter 12.3, Problem 89E

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The set theory explanation to the arrangement of numbers in each row of Pascal’s triangle is symmetric.

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Chapter 12.3, Problem 88E

Chapter 12.4, Problem 1E

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Chapter 12 Solutions

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The set theory explanation to the arrangement of numbers in each row of Pascal’s triangle is symmetric.

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To explain:

The set theory explanation to the arrangement of numbers in each row of Pascal’s triangle is symmetric.