EXPLANATION:
Given;
We are told that Matilda has 9 books and she wants to give 3 of these to her sister as a gift.
Required;
We are required to calculate how many different gifts are possible.
Step-by-step solution;
To determine how many gifts of 3 different books can be given out by Matilda, we will use the formula for combinations which is;
[tex]_nC_r=\frac{n!}{r!(n-r)!}[/tex]
Therefore, to determine the combination of 3 books out of a total of 9;
[tex]\begin{gathered} _9C_3=\frac{9!}{3!(9-3)!} \\ \\ _9C_3=\frac{9\times8\times7\times...\times1}{3\times2\times1(6\times5\times4\times...\times1)} \\ \\ _9C_3=84 \end{gathered}[/tex]
Therefore, there is a total of 84 different gifts
ANSWER
84
