Lee wants to hang 8 of his 20 photos in an ordered line on the wall above his desk. How many ways can he do this?
Unitary Method
The word “unitary” comes from the word “unit”, which means a single and complete entity. In this method, we find the value of a unit product from the given number of products, and then we solve for the other number of products.
Speed, Time, and Distance
Imagine you and 3 of your friends are planning to go to the playground at 6 in the evening. Your house is one mile away from the playground and one of your friends named Jim must start at 5 pm to reach the playground by walk. The other two friends are 3 miles away.
Profit and Loss
The amount earned or lost on the sale of one or more items is referred to as the profit or loss on that item.
Units and Measurements
Measurements and comparisons are the foundation of science and engineering. We, therefore, need rules that tell us how things are measured and compared. For these measurements and comparisons, we perform certain experiments, and we will need the experiments to set up the devices.
![**Simplify each binomial coefficient or permutations to factorial fractions:**
\[
\binom{n}{k} = \frac{n!}{(n-k)!k!} \quad \quad P(n,k) = \frac{n!}{(n-k)!}
\]
You need not simplify these expressions, such as \(15^4\) or \(17!\), in your response.
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**Photos and Money**
- Lee wants to hang 8 of his 20 photos in an ordered line on the wall above his desk. How many ways can he do this?
- Lee wants to select 9 photos of his 20 to take on a trip. How many ways can he do this?
- Lee has decided to give his collection of 20 unique photographs to his three children. In how many ways can he partition his photo collection among these three children where it may be that some children get no photographs?
- Lee also has 500 dollars he wants to give his three children. In how many ways can he divide it among his three children? It may be the case that a child receives no money.
- Lee’s children will be upset if he doesn’t give each of them at least 50 dollars. How many ways can Lee partition his money so his children won’t be upset?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F10732faa-f9b7-4c12-81f1-19b5d255f419%2Fbadbd0c8-14cb-418d-8b3d-11bb1081d3f3%2F2wv1d1_processed.png&w=3840&q=75)
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