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Question
If `""^("n" - 1)"P"_4 : ""^"n""P"_5` = 1 : 6, then n = ______.
Options
6
`1/6`
12
`1/12`
MCQ
Fill in the Blanks
Solution
If `""^("n" - 1)"P"_4 : ""^"n""P"_5` = 1 : 6, then n = 6.
Explanation:
`""^("n" - 1)"P"_4 : ""^"n""P"_5` = 1 : 6
∴ `1/6 = (""^("n" - 1)"P"_4)/(""^"n""P"_5)`
= `(("n" - 1)!)/("n"!)`
= `(("n" - 1)!)/("n"("n" - 1)!)`
⇒ n = 6
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Permutations - Properties of Permutations
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