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PERMUTATIONS AND COMBINATIONS — MATHS STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceMATHSPERMUTATIONS AND COMBINATIONS1 Mark
Question
Find the value of n such that: $\frac{^{n} \mathrm{P}_{4}}{^{n-1} \mathrm{P}_{4}}=\frac{5}{3}, n>4$
✓

Answer

Here, $\frac{^{n} \mathrm{P}_{4}}{^{n-1} \mathrm{P}_{4}}=\frac{5}{3}$
Thus, 3n (n – 1) (n – 2) (n – 3) = 5(n – 1) (n – 2) (n – 3) (n – 4)
or 3n = 5 (n – 4) [as (n – 1) (n – 2) (n – 3) $\ne$ 0, n > 4]
or n = 10

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