Question

PLEASE HELP

Answer 1

Answer:

There are 24 ways to select one book of each type.

Step-by-step explanation:

In mathematics, the procedure to select k items from n distinct items, without replacement, is known as combinations.

The formula to compute the combinations of k items from n is given by the formula:

${n\choose k}=\frac{n!}{k!(n-k)!}$

It is provided that there are 6 different biographies and 4 different mystery novels on a bookshelf.

Compute the number of ways to select a biography as follows:

Number of ways to select a biography =

$={6\choose 1}\\\\=\frac{6!}{1!(6-1)!}\\\\=\frac{6\times 5!}{1\times 5!}\\\\=6$

There are 6 ways to select a biography.

Compute the number of ways to select a mystery novel as follows:

Number of ways to select a mystery novel =

$={4\choose 1}\\\\=\frac{4!}{1!(4-1)!}\\\\=\frac{4\times 3!}{1\times 3!}\\\\=4$

There are 4 ways to select a mystery novel.

Then the total number of way to select one book of each type is:

${6\choose 1}\times {4\choose 1}=6\times 4=24$

Thus, there are 24 ways to select one book of each type.