Find n if n 1p3 np4 1 9

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If n-1p3:np4=1:9,find n

Answered by admin @


Answer:

n = 9

Step-by-step explanation:

^{n-1}P_{3} \: : \: ^{n}P_{4} = 1 \: : \: 9\\\\\\\implies \dfrac{(n-1)!}{(n-1-3)!} \div \dfrac{(n)!}{(n-4)!} = 1 \div 9\\\\\\\implies \dfrac{(n-1)! \times (n-4)!}{(n-4)! \times (n)!} = \dfrac{1}{9}\\\\\\\implies \dfrac{(n-1)!}{n(n-1)!} = \dfrac{1}{9}\\\\\\\implies \dfrac{1}{n} = \dfrac{1}{9}\\\\\\\implies n = 9\\\\\\\boxed{\boxed{\underline{\boxed{\bold{n = 9}}}}}

Properties Used:

1. \; ^nP_r = \dfrac{n!}{(n-r)!}

And

2. \; n! = n(n-1)!


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