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NCERT Class XI Mathematics - Permutations and Combinations - Solutions

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Question : 16
Total: 41
Find n if
n−1
‌
P3 :
n
‌
P4 = 1 : 9
Solution:  
We have,
n−1
‌
P3 :
n
‌
P4 = 1 : 9
⇒
(n−1)!
(n−1−3)!
 :
n!
(n−4)!
 = 1 : 9 ⇒
(n−1)!
(n−4)!
×
(n−4)!
n!
 =
1
9
⇒
(n−1)!
n(n−1)!
 =
1
9
 ⇒
1
n
 =
1
9
 ⇒ n = 9
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