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A set s contains 6 elements, how many different subsets can be form the elements of s that will contain exactly 4 elements

User Samba
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The binomial coefficient
\binom{n}{k} express exactly the number of ways you can choose k elements from a set of n elements. It is defined as


\binom{n}{k} = (n!)/(k!(n-k)!)

where n! express the factorial of n, which is defined as the multiplication of all number from n to 2:


n! = n* (n-1) * (n-2) * \ldots * 3 * 2

So, in your case, the number of subset of cardinality 4 that you can extract from a set of cardinality 6 is


\binom{6}{4} = (6!)/(2!4!) = (6*5*4*3*2)/(2*4*3*2) = (6*5)/(2) = 3*5=15

User Tsanyo Tsanev
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