Question

The value of n, if nCn-2 = 15.​

Answer 1

Answer:

Step-by-step explanation:

we know that nCr is the general formula for combination.

so ,here, nCn-2=nCr,that means

r=n-2(equation 1)

now we know the formula of nCr=n!/r!(n-r)!

so nCn-2=n!/r!(n-r)! (equation 2)

substituting equation 1 in equation 2:

nCn-2=n!/(n-2)!(n-(n-2))!⇒

n!/(n-2)!(2!)

we know that we can write n! as =n(n-1)(n-2)!

so =n(n-1)(n-2)!/(n-2)!(2!)⇒n(n-1)/2×1⇒

so it is given n(n-1)/2=15⇒

n²-n-30=0

n²-6n+5n-30=0

⇒n(n-6)+5(n=6)

⇒(n+5)(n-6)=0

so that means n=-5 or n=6

but u know when we are considering permutation and combination,n is always positive.

so n=6

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