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Illusion [34]
3 years ago
14

How many combinations exist of the letters w, x, y, z, taking two at a time?

Mathematics
1 answer:
Sindrei [870]3 years ago
3 0

The binomial coefficient

\displaystyle \binom{4}{2} = \dfrac{4!}{2!(4-2)!} = \dfrac{4\cdot 3}{2} = 2\cdot 3 = 6

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.

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