If ^nP_r = ^nP_r+1 and ^nC_r = ^nC_r-1, then the value of r is equal to:

Question

If $^nP_r = {}^nP_{r+1}$ and $^nC_r = {}^nC_{r-1}$, then the value of $r$ is equal to:

Accepted Answer

From $^nP_r={}^nP_{r+1}$: $\dfrac{n!}{(n-r)!}=\dfrac{n!}{(n-r-1)!} \Rightarrow n-r=1$ \ldots (i)

From $^nC_r={}^nC_{r-1}$: $n-r+1=r$ \ldots (ii)

From (i): $n-r=1$, substituting into (ii): $1+1=r \Rightarrow r=2$

Solutions · 1