Question:

Is 3! + 4! = 7! ?

Updated On: Oct 21, 2023
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Solution and Explanation

3! = 1 x 2 x 3 = 6 
4! = 1 x 2 x 3 x 4 = 24
∴ 3! + 4! = 6 + 24 = 30 
7! = 1 x 2 x 3 x 4 x 5 x 6 x 7 = 5040 
∴ 3! + 4! ≠ 7!

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Concepts Used:

Permutations and Combinations

Permutation:

Permutation is the method or the act of arranging members of a set into an order or a sequence. 

  • In the process of rearranging the numbers, subsets of sets are created to determine all possible arrangement sequences of a single data point. 
  • A permutation is used in many events of daily life. It is used for a list of data where the data order matters.

Combination:

Combination is the method of forming subsets by selecting data from a larger set in a way that the selection order does not matter.

  • Combination refers to the combination of about n things taken k at a time without any repetition.
  • The combination is used for a group of data where the order of data does not matter.