find n if n! ÷2!(n-2)! and n! ÷4!(n-4)! are in the ratio 2:1
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n!=6!
Step-by-step explanation:
n!÷2!(n-2)! : n!÷4!(n-4)!
=> n!/2!(n-2)! : n!/4!(n-4)!=2:1
=> n²!/2!-n! : n²!/4-!n!=2:1
=> (n²/2-n)!/(n²/4-n)!=2!/1!
=> (n²-2n)!/(n²-4n)!=2!/1!
=> n²!-2n!=(n²-4n)!×2!
=> n²!-2n!=2n²!-8n!
=> n!(n-2)!=2n!(n-4)!
=> n!-2!=2!(n-4)!
=> n!-2!=2n!-8!
=> n!-2n!=-8!+2!
=> -n!=-6!
=> n!=6!
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