Question

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

Answer 1

ANSWER:

792

STEP-BY-STEP 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:

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

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

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

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