Anonymous

# What does two numbers on top of each other and in a parenthesis mean?

I've found it in statistics work, and don't believe it means division or fractions, because there is not line separating the two so I'm lost. The situation I'm describing I've found, more specifically, when dealing with factorials and probability questions. Any help is greatly appreciated.

Relevance

Combination.

It can also be written

C(n, k)

(where n and k are numbers)

It is the number of ways that you can pick k objects, out of a collection of n objects.

C(n, k) = n! / k!(n-k)!

where ! means "factorial"

as in 5! = 1*2*3*4*5 = 120

C(5, 2) = 5!/ 2!3! = 120/(2*6) = 10

This would be written as a set of big parentheses, with a 5 on top of the 2, no bar between them).

There are ten ways to pick two objects out of a collection of five:

five objects: ABCDE

10 possible doublets: AB AC AD AE BC BD BE CD CE DE

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Very convenient to calculate the odds in a lottery.

A lottery picks 6 numbers out of 49. The number of possible combinations are:

C(49, 6) = 49! / 6!43! = 13,983,816

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• Anonymous

This is called "choose notation." For example, if you see

(5)

(3)

(except that there should be only one set of large parenthesis surrounding them), this is called "5 choose 3."

"5 choose 3" is the number of ways to select 3 objects out of 5 objects total. It is equal to 5! / [(3!) (5 - 3)!] = 10.

In general,

(n)

(k)

is equal to n! / (k! * (n -k)!).

This is because, in order to choose k objects from a total of n, we could arrange them in a row and say that we're selecting the first k objects in the row. There's n! ways to arrange n objects in a row.

However, once we have arranged the n objects in a row, permuting the first k objects won't change which choice we've made (because they're still the first k objects), and permuting the last (n - k) objects won't change which choice we've made (because the last (n - k) objects still won't be within the first k objects), so we need to divide by k! and (n - k)! to avoid counting the same choice multiple times.

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• its called combination

should look like thise

(n)

(x)

meaning n choose x.

check here for more details, http://en.wikipedia.org/wiki/Combination

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