- #1
Bachelier
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How many sequences of zeros and ones of length 7 contain exactly 4 ones and 3 zeros?
I'm having a hard time figuring out why it is 7 Chooses 4?
thx
I'm having a hard time figuring out why it is 7 Chooses 4?
thx
Bacle said:Can
you see, in the context of this problem , why 7C4=7C3?
Bacle said:Exactly. Perfect. This is the general identity nCk =nC(n-k).
Bachelier said:How many sequences of zeros and ones of length 7 contain exactly 4 ones and 3 zeros?
I'm having a hard time figuring out why it is 7 Chooses 4?
thx
"7 Choose 4" is a mathematical notation that represents the number of ways to choose 4 objects from a set of 7 objects, without regard to their order. It is also known as a combination and is denoted as "C(7,4)" or "7C4".
The formula for calculating "7 Choose 4" is nCr = n! / (r! * (n-r)!), where n is the total number of objects and r is the number of objects to be chosen. In this case, it would be 7! / (4! * (7-4)!) = 35.
A combination is a selection of objects without regard to their order, while a permutation is a selection of objects with regard to their order. In other words, combinations are about choosing a group of objects, while permutations are about arranging a group of objects.
"7 Choose 4" can be applied in various real-life situations, such as selecting a team of 4 players out of a group of 7, choosing 4 items from a menu of 7 options, or picking 4 books from a shelf of 7 books. It can also be used in probability calculations and in solving certain types of counting problems.
Yes, the formula for calculating combinations is nCr = n! / (r! * (n-r)!), where n is the total number of objects and r is the number of objects to be chosen. This formula can be used to calculate combinations for any values of n and r, as long as n is greater than or equal to r and both n and r are positive integers.