n!
n!
EXAMPLE 6 If
and
2!(n − 2)!
are in the ratio 2 : 1, find the value of n.
4!(n-4)!
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Answer:
Given,
2!(n−2)!
n!
:
4!(n−4)!
n!
=2:1
⇒
2!(n−2)!
n!
×
n!
4!(n−4)!
=
1
2
⇒
2!(n−2)
4!(n−4)!
=2
⇒
2!
4×3×2!
×
(n−2)(n−3)(n−4)!
4!(n−4)!
=2
⇒12=2(n−2)(n−3)
⇒6=n
2
−5n+6
⇒n
2
−5n=0
⇒n(n−5)=0
⇒n=0 or 5
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