Question

12. if 5Pr = 60, then the value of r is
a) 3
b) 2​

Answer 1

Answer:

⇒ $r=3$

Step-by-step explanation:

Given :

$_5P_r = 60$

Find r.

Solution :

We know that,

$_nP_r = \frac{n!}{(n-r)!}$

⇒ $_5P_{r} = 60 = \frac{5!}{(5-r)!}$

⇒ $\frac{5!}{(5-r)!} = 60$

⇒ $1 \times 2 \times 3 \times 4 \times 5 = 60 \times (5-r)!$

⇒ $120 = 60 \times (5-r)!$

⇒ $\frac{120}{60} = (5-r)!$

⇒ $2 = (5 - r)!$

⇒ $1 \times 2 = (5 - r)!$

⇒ $2! = (5-r)!$

⇒ $2 = 5-r$

⇒ $2 - 5 = -r$

⇒ $-3 =-r$

⇒ $r=3$

Answer 2

Answer:

r=3

Step-by-step explanation:

Given : $^5P_r=60$

To Find : value of r

Solution:

Formula : $^nP_r=\frac{n!}{(n-r)!}$

Substitute n = 5

$^5P_r=\frac{5!}{(5-r)!}$

We are given that $^5P_r=60$

So, $60=\frac{5!}{(5-r)!}$

$60=\frac{5!}{(5-r)!}$

$5  \times  4  \times 3  \times  2  \times 1  = 60 \times (5-r)!$

$120 = 60 \times (5-r)!$

$2= (5-r)!$

$2 \times 1= (5-r)!$

$2!= (5-r)!$

$2=5-r$

$2=5-rr=3$

Hence the value of r is 3