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NCERT Class XI Mathematics - Permutations and Combinations - Solutions

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Question : 16 of 41
Marks: +1, -0
Find n if  n−1P3\,{}^{n-1}P_3 :  nP4\,{}^{n}P_4 = 1 : 9
Solution:  
We have,  n−1P3\,{}^{n-1}P_3 :  nP4\,{}^{n}P_4 = 1 : 9
⇒ (n−1)!(n−1−3)!\frac{(n-1)!}{(n-1-3)!} : n!(n−4)!\frac{n!}{(n-4)!} = 1 : 9 ⇒ (n−1)!(n−4)!×(n−4)!n!\frac{(n-1)!}{(n-4)!} \times \frac{(n-4)!}{n!} = 19\frac{1}{9}
⇒ (n−1)!n(n−1)!\frac{(n-1)!}{n(n-1)!} = 19\frac{1}{9} ⇒ 1n\frac{1}{n} = 19\frac{1}{9} ⇒ n = 9
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