There are 10 different selections of 3 notebook styles are possible.
We can answer the question with the combinations formula.
First we determine that Antonie has to select 3 notebooks from 3 different styles (a,b,c).
We generally denote Combinations with nCk.
However, when we need to select 'k' number of item from 'n' styles, the formula changes to:
[tex] (n+k-1)C(k-1) [/tex]
Substituting the values from the question in the equation we have,
[tex] (3+3-1)C(3-1) [/tex], which gives us
[tex] 5C2 [/tex]
Now, we use the combinations formula to arrive at the final answer.
[tex] nCr = \frac{n!}{r!(n-r)!} [/tex]
Substituting the values from above in the equation we have,
[tex] 5C2 = \frac{5!}{2!(5-2)!} [/tex]
[tex] 5C2 = 10 [/tex]
