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NCERT Class XI Mathematics - Permutations and Combinations - Solutions

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Question : 23
Total: 41
Determine n if
(i)
2n
‌
C3 :
n
‌
c3 = 12 : 1 (ii)
2n
‌
C3 :
n
‌
C3 = 11 : 11
Solution:  
(i)
2n
‌
C3 :
n
‌
c3 = 12 : 1
⇒
2n
‌
C3
n
‌
C3
 =
12
1
 ⇒
2n!
3!(2n−3)!
 ×
3!(n−3)!
n!
 = 12
⇒
2n(2n−1)(2n−2)
n(n−1)(n−2)
 = 12 ⇒
4(2n−1)
n−2
 = 12 ⇒ 8n - 4 = 12 n - 24 ⇒ n = 5
(ii)
2n
‌
C3 :
n
‌
C3 = 11 : 11
⇒
2n
‌
C3
n
‌
C3
 = 11 ⇒
2n!
3!(2n−3)!
 ×
3!(n−3)!
n!
 = 11
⇒
2n(2n−1)(2n−2)
n(n−1)(n−2)
 = 11 ⇒
4(2n−1)
n−2
 = 11 ⇒ 8n - 4 = 11 n - 22 ⇒ n = 6
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