Question

Act a bin contains 100 style a notebooks, 100 style b notebooks, and 100 style c notebooks. antoine will select 3 notebooks from the bin. how many different selections of 3 notebook styles are possible?

Answer 1

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:

$(n+k-1)C(k-1)$

Substituting the values from the question in the equation we have,

$(3+3-1)C(3-1)$, which gives us

$5C2$

Now, we use the combinations formula to arrive at the final answer.

$nCr = \frac{n!}{r!(n-r)!}$

Substituting the values from above in the equation we have,

$5C2 = \frac{5!}{2!(5-2)!}$

$5C2 = 10$