Question

Suppose we want to choose 7 letters, without replacement, from 12 distinct letters.

Answer 1

792

Explanation:

Since there is no replacement and we assume that the order does not matter, we must use the combination formula, which is the following:

`_nC_r=(n!)/(r!(n-r)!)`

In this case n = 12 and r = 7, we substitute each value:

`\begin{gathered} _(12)C_7=(12!)/(7!(12-7)!)=(12!)/(12!\cdot7!) \\ \\ _(12)C_7=792 \end{gathered}`

This means that there are a total of 792 different ways to choose 7 letters from 12 distinct letters.