Combinations determine the number of possible arrangements in a collection of items where order does not matter. A combination can select items in any order, unlike permutations where order is important. Pascal's triangle arises in probability, combinatorics, and algebra. It is constructed by adding the numbers above and to the left and right of each entry, with blank entries treated as zero.

1. O l i v i a
Mathrmatics

3. Combination
Whatiscombination？
Acombinationisamathematical
techniquethatdeterminesthenumber
ofpossiblearrangementsinacollection
ofitemswheretheorderoftheselection
doesnotmatter.Incombinations,you
canselecttheitemsinanyorder.
Combinationscanbeconfusedwith
permutations.
Exampleofcombination:

5. In how many ways can seven books be arranged on a shelf?
Solution:
Number of ways in which the first book can be placed = 7
Number of ways in which the second book can be placed = 6
Similarly,
The total number of ways in which seven books can be arranged on a shelf = 7 × 6 × 5 × 4 × 3
× 2 × 1 (i.e., 7!)
= 5040
Learning time:

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9. A permutation is an act of arranging objects or
numbers in order. Combinations are the way of
selecting objects or numbers from a group of
objects or collections, in such a way that the order
of the objects does not matter.
What is the difference between
combination and permutation?

10. Pascal's triangle
In mathematics, Pascal's triangle is a triangular array of the binomial coefficients
that arises in probability theory, combinatorics, and algebra. In much of the Western
world, it is named after the French mathematician Blaise Pascal, although other
mathematicians studied it centuries before him in India,Persia, China, Germany, and
Italy.
The rows of Pascal's triangle are conventionally enumerated starting with row at the
top (the 0th row). The entries in each row are numbered from the left beginning with
and are usually staggered relative to the numbers in the adjacent rows. The triangle
may be constructed in the following manner: In row 0 (the topmost row), there is a
unique nonzero entry 1. Each entry of each subsequent row is constructed by adding
the number above and to the left with the number above and to the right, treating
blank entries as 0. For example, the initial number of row 1 (or any other row) is 1 (the
sum of 0 and 1), whereas the numbers 1 and 3 in row 3 are added to produce the
number 4 in row 4.

11. Reflection
Through this unit, I learned What is the difference between combination and persistence. And
the definition of combination and persistence. How to solve this problem. The biggest
challenge for me is how to balance the collection of works and pre calculus, which I do poorly.
In the next semester, I will change myself

12. Thanks
for
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