Jaime had ten posters, but only five could fit on his closet door. how many

Mathematics

1 answer:

sukhopar [10]2 years ago

5 0

There are 30240 different ways can he arrange the five posters out of the ten on his closet door

<h3>How to determine the number of arrangements?</h3>

The given parameters are:

Total, n = 10
Posters to arrange, r = 5

The number of ways is calculated as:

Ways = $^nP_r$

This gives

Ways = $^{10}P_5$

Apply the permutation formula

Ways = 30240

Hence, there are 30240 different ways can he arrange the five posters out of the ten on his closet door

You might be interested in

A small plane and a large plane are 6.8km from each other, at the same altitude (height). From an observation tower, the two air

Lemur [1.5K]

Answer:

7.9km

Step-by-step explanation:

(a)See attached for the diagram representing this situation.

(b)

In Triangle ABC

$\text{Using Law of Sines}\\\dfrac{\sin A}{a}=\dfrac{\sin C}{c} \\\dfrac{\sin A}{5.2}=\dfrac{\sin 58^\circ}{6.8} \\\sin A=5.2 \times \dfrac{\sin 58^\circ}{6.8}\\A=\arcsin (5.2 \times \dfrac{\sin 58^\circ}{6.8})\\A=40.43^\circ$

Next, we determine the value of Angle B.

$\angle A+\angle B+\angle C=180^\circ\\40.43+58+\angle B=180^\circ\\\angle B=180^\circ-(40.43+58)\\\angle B=81.57^\circ$

Finally, we find b.

$\text{Using Law of SInes}\\\dfrac{b}{\sin B}=\dfrac{c}{\sin C} \\\dfrac{b}{\sin 81.57^\circ}=\dfrac{6.8}{\sin 58^\circ} \\b=\dfrac{6.8}{\sin 58^\circ} \times \sin 81.57^\circ\\b=7.9km $ (to the nearest tenth of a kilometer)$