please help , you can use the formula see if help **Package Delivery**A delivery driver has 10 *unique* packages to deliver.---**i** How many ways can the delivery driver select 6 of these packages to deliver?**ii** How many ways can the delivery driver select 4 of these packages to discard while delivering the rest? Explain how this problem relates to the first subproblem.**iii** How many different routes may the delivery truck drive to deliver 8 of the 10 packages? A route is an ordered sequence of destinations. You may assume each package may only be delivered to its unique destination.**iv** Before leaving for the day, the delivery trucks are loaded with packages. How many ways can 120 *unique* packages be loaded into 10 delivery trucks where some trucks may have no packages?**v** How many ways can 120 *identical* packages be loaded into 10 delivery trucks where some trucks may have no packages?**vi** The delivery truck driver union is concerned that the workload is unequal. How many ways can 120 *identical* packages be loaded into 10 delivery trucks where each truck must have at least 5 packages?**vii** How many ways can 120 *unique* packages be loaded into 10 delivery trucks where each truck must have the same number of packages? The image shows two mathematical expressions commonly used in combinatorics:1. **Binomial Coefficient**: \[ \binom{n}{k} = \frac{n!}{(n-k)!k!} \] This expression represents the number of ways to choose \(k\) elements from a set of \(n\) elements, without considering the order of selection. Here, \(n!\) (n factorial) is the product of all positive integers up to \(n\).2. **Permutation**: \[ P(n, k) = \frac{n!}{(n-k)!} \] This represents the number of ways to arrange \(k\) elements out of a set of \(n\) elements, taking order into account.In these formulas:- \(n\) is the total number of elements.- \(k\) is the number of elements to select or arrange.- \(n!\) denotes the factorial of \(n\), which is the product \(n \times (n-1) \times \ldots \times 1\).- \((n-k)!\) and \(k!\) are similar factorial expressions for \(n-k\) and \(k\) respectively.

Name: please help , you can use the formula see if help **Package Delivery**
Uploaded: 2024-03-20T06:47:08.000Z
Channel: Bartleby
Description: please help , you can use the formula see if help **Package Delivery**A delivery driver has 10 *unique* packages to deliver.---**i** How many ways can the delivery driver select 6 of these packages to deliver?**ii** How many ways can the delivery dri