Find n if (n-3)!/(n-5)! = 2
Answers
Answered by
0
Answer:
THE ANSWER IS
N = 5 OR N = 7
Step-by-step explanation:
N-3 = 2 / N-5 = 2
N = 2+3 / N = 2+5
N = 5 / N = 7
Answered by
1
Answer:
5
Step-by-step explanation:
Using the property n! = n×(n-1)×(n-2)!
(n-3)! can be written as (n-3)(n-3-1)(n-3-2)!
= (n-3)(n-4)(n-5)!
Now the question becomes -
(n-3)(n-4)(n-5)!/(n-5)! = 2
=> (n-3)(n-4) = 2
=> n²-4n-3n+12 = 2
=> n²-7n+10 = 0
Factorising
n²-(5+2)n+10 = 0
n²-5n-2n+10 = 0
n(n-5)-2(n-5) = 0
(n-5)(n-2) = 0
=> n=5 or n=2
But on putting n=2, the terms inside factorial becomes negative so it is not possible, hence n=5 is the only value
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