Question

9P5+5×9P4=10Pr find r

Answer 1

9p5=9!/(9-5)!=9!/4!
9p4=9!/(9-4)!=9!/5!
now use the equation.
9!/4!+5×9!/5!=10pr
now solve it.
when you will get something p something=10pr
then by comparison you can tell r =something that you will get

Answer 2

Answer :

We have,

$\sf \qquad \: {}^{9}P_5 + 5. {}^{9} P_4 = {}^{10}P _r \\ \\ \rightarrow \tt \frac{9!}{(9! - 5!)} + 5. \frac{9!}{(9 - 4)!} = \frac{10!}{(10 - r)!} \\ \\ \rightarrow \tt \frac{9!}{4!} + 5. \frac{9!}{5!} = \frac{10!}{(10 - r)!} \\ \\ \rightarrow \tt \frac{9!}{4!} + \frac{9!}{4!} = \frac{10!}{(10 - r)!} \\ \\ \rightarrow \tt \: 2 \times \frac{9!}{4!} = \frac{10!}{(10 - r)!} \\ \\ \rightarrow \tt \frac{5 \times 2 \times 9!}{5 \times 4!} = \frac{10!}{(10 - r)!} \\ \\ \tt \rightarrow \frac{10 \times 9!}{5!} = \frac{10!}{(10 - r)!} \\ \\ \rightarrow \tt \frac{10!}{5!} = \frac{10!}{(10 - r)!} \\ \\ \rightarrow \tt(10 - r)! = 5! \\ \\ \rightarrow \tt10 - r = 5 \\ \\ \implies \tt \: r = 5$