Question

If 5.4Pr=6.5Pr-1 then find r

Answer 1

Answer:

r = 3

5 * ⁴P₃  = 6 * ⁵P₂

Step-by-step explanation:

Replacing r with a

Question is

5 * ⁴Pₐ = 6 * ⁵Pₐ₋₁   find a

=> 5  *  4!/(4 - a)!  = 6 * 5!/(5 - (a-1))!

=> 5! /(4 - a)! = 6 * 5! /(6 - a)!

=> (6 - a)! = 6 * (4 - a)!

=>  (6 - a)(5 - a) (4 - a)! = = 6 * (4 - a)!

=>  (6 - a)(5 - a)  = 6

=> a² - 11a + 30 = 6

=> a² - 11a + 24 = 0

=> a² - 3a - 8a  + 24 = 0

=> (a - 3)(a - 8) = 0

=> a = 3 or 8

but a should be less than 4 & 5

=> a = 3

5 * ⁴P₃  = 6 * ⁵P₂ = 120

Answer 2

Answer:

The Correct answer is r = 3

5 * ⁴P₃  = 6 * ⁵P₂

Procedure:

Let us replace r with a

Now the final equation to be solved is

5 * ⁴Pₐ = 6 * ⁵Pₐ₋₁   find a

=> 5  *  4!/(4 - a)!  = 6 * 5!/(5 - (a-1))!

=> 5! /(4 - a)! = 6 * 5! /(6 - a)!

=> (6 - a)! = 6 * (4 - a)!

=>  (6 - a)(5 - a) (4 - a)! = = 6 * (4 - a)!

=>  (6 - a)(5 - a)  = 6

=> a² - 11a + 30 = 6

=> a² - 11a + 24 = 0

=> a² - 3a - 8a  + 24 = 0

=> (a - 3)(a - 8) = 0

=> a = 3 or 8

But, as per the equation the value of a should be less than 4 & 5

=> a = 3

5 * ⁴P₃  = 6 * ⁵P₂ = 120