Question

Find the number of ways of choosing 3 books from a shelf holding 5 different books

Answer 1

To find the number of ways to choose 3 books from a shelf holding 5 different books, we can use the combination formula, which is given by:

\[
\binom{n}{r} = \frac{n!}{r!(n - r)!}
\]

In this case, \( n = 5 \) (the total number of books) and \( r = 3 \) (the number of books to choose). Plugging in these values, we get:

\[
\binom{5}{3} = \frac{5!}{3!(5 - 3)!} = \frac{5!}{3! \cdot 2!}
\]

Now calculating the factorials:

\[
5! = 5 \times 4 \times 3 \times 2 \times 1 = 120
\]
\[
3! = 3 \times 2 \times 1 = 6
\]
\[
2! = 2 \times 1 = 2
\]

Now substituting these values into the combination formula:

\[
\binom{5}{3} = \frac{120}{6 \cdot 2} = \frac{120}{12} = 10
\]

Thus, the number of ways to choose 3 books from a shelf holding 5 different books is \( \boxed{10} \).