Question

9P5+9P4=10Pr.find r solve it.

Answer 1

9p5+9p4=10pr
45p+36p=10pr
81p=10pr
r=8.1

Answer 2

Answer:

The value of r = 4.705.

Step-by-step explanation:

We are given the equation, $9_{P_{5}}+9_{P_{4}}=10_{P_{r}}$

Now, $n_{P_{r}=\frac{n!}{(n-r)!}$

So, we get,

$9_{P_{5}}+9_{P_{4}}=10_{P_{r}}$

i.e. $\frac{9!}{(9-5)!}+\frac{9!}{(9-4)!}=\frac{10!}{(10-r)!}$

i.e. $\frac{9!}{4!}+\frac{9!}{5!}=\frac{10!}{(10-r)!}$

i.e. $9\times 8\times 7\times 6\times 5+9\times 8\times 7\times 6=\frac{10!}{(10-r)!}$

i.e. $15120+3024=\frac{10!}{(10-r)!}$

i.e. $18144=\frac{3628800}{(10-r)!}$

i.e. $(10-r)!=\frac{3628800}{18144}$

i.e. $(10-r)!=200$

As, we know, $5!=120$ and $6!=720$

So, $120<200<720$

i.e. $5!<(10-r)!<6!$

i.e. $5<(10-r)<6$

i.e. $-5<-r<-4$

i.e. $4<r<5$

So, from the graph, the value of r = 4.705.