Prove that: 2 5P3= nP4

Prove that: 2.⁵P₃= ⁿP₄

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Please find below the solution to the asked query :

Assuming that here we have to find the value of n 2 . {}^{5}P_{3} = {}^{n}P_{4} 2 \times \frac{5!}{(5 - 3)!} = \frac{n!}{(n - 4)!} \frac{2 \times 5 \times 4 \times 3 \times 2!}{2!} = \frac{n \times (n - 1) \times (n - 2) \times (n - 3) \times (n - 4)!}{(n - 4)!} 5 \times 4 \times 3 \times 2 = n \times (n - 1) \times (n - 2) \times (n - 3) So, on comparing n = 5 . Value of n is 5 .

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