Question

Solve for n if:
$\frac{(15-n)!}{(12-n)!}=5!$

Answer 1

15-n/12-n = 5

15-n = 5(12-n)

15-n = 60-5n

4n = 45

n = 45/4

Answer 2

Answer:

9

Step-by-step explanation:

As per the question,

We have given the equation,

$\frac{(15 - n)!}{(12 - n)!}=5!$

$\frac{(15 - n)(14 - n)(13 - n)(12 - n)!}{(12 - n)!}=5 \times 4 \times 3 \times 2 \times 1$

(15 - n)(14 - n)(13 - n) = 5 × 4 × 3 × 2

Let (13 - n ) = x

Therefore,

(2 + x) (1 + x) x = 6 × 5 × 4

(2 + x) (1 + x) x = (2 + 4) × (1 + 4) × 4

∴ x = 4

13 - n = 4

∴ n = 9

Hence, the value of n = 9