The binomial coefficient
[tex] \displaystyle \binom{4}{2} = \dfrac{4!}{2!(4-2)!} = \dfrac{4\cdot 3}{2} = 2\cdot 3 = 6 [/tex]
Tells you that there are 6 ways of choosing a subset of two letters from the four given letters.
For each of these subsets there are two combinations (you can interchange the two letters: say that you choose the subset wz, you have the two combinations wz and zw)
So, there is a total of 12 combinations of the letters w, x, y, z, taking two at a time.
There are 6 ways of choosing a subset of two letters from the four given letters.
The arrangement of the different things or numbers in a number of ways is called the combination.
For each of these subsets there are two combinations (you can interchange the two letters: say that you choose the subset wz, you have the two combinations wz and zw)
So, there is a total of 6 combinations of the letters w, x, y, z, taking two at a time.
The combination will be calculated as:-
[tex]^4C_2=\dfrac{4!}{2!(4-2)!}[/tex]
[tex]^4C_2=\dfrac{4\times 3}{2}[/tex]
[tex]^4C_2=6[/tex]
Therefore there are 6 ways of choosing a subset of two letters from the four given letters.
To know more about combinations follow
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