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 this 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 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 this 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.

Name: Simplify each binomial coefficient or permutations to factorial fract
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Description: Simplify each binomial coefficient or permutations to factorial fractions:n!n!P(n, k) =(n – k)!k!(n – k)!You need not simplify these expressions, such as 15' or 17!, in your response.Photos and MoneyinyLee wants to select 9 photos of his 20 to take

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Concept explainers

Permutations and Combinations

If there are 5 dishes, they can be relished in any order at a time. In permutation, it should be in a particular order. In combination, the order does not matter. Take 3 letters a, b, and c. The possible ways of pairing any two letters are ab, bc, ac, ba, cb and ca. It is in a particular order. So, this can be called the permutation of a, b, and c. But if the order does not matter then ab is the same as ba. Similarly, bc is the same as cb and ac is the same as ca. Here the list has ab, bc, and ac alone. This can be called the combination of a, b, and c.

Counting Theory

The fundamental counting principle is a rule that is used to count the total number of possible outcomes in a given situation.

Topic Video

Question

Simplify each binomial coefficient or permutations to factorial fractions:
n!
n!
P(n, k) =
(n – k)!k!
(n – k)!
You need not simplify these expressions, such as 15' or 17!, in your response.
Photos and Money
iny
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 this 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?

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