Question

Best Buy is displaying 15 laptops for a big store sale. The laptops include 6 identical​ Dells, 4 identical​ Chromebooks, and 5 identical Macbooks. They must all be ordered on counter from front to back. How many ways can these 15 laptops be​ ordered?

Answer 1

630,630 different arrangements are possible for the given laptops.

Explanation:

Total number of laptops = n = 15

Number of identical Dell laptops = 6

Number of identical Chromebooks = 4

Number of identical Mackbooks = 5

We have to find in how many ways can the laptops be arranged. Number of arrangement of objects is calculated using Permutations as the order of objects matter during the arrangement. The formula to calculate the number of possible arrangements when there are similar objects is given as:

`(n!)/(a!b!c!...)`

Here n is the total number of objects and a,b, and c represent the number of identical objects. Using the given values we get:

`(15!)/(6!4!5!) = 630630`

This means 630,630 different arrangements are possible for the given laptops.