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Alborosie
3 years ago
11

PLEASE HELP

Mathematics
1 answer:
enyata [817]3 years ago
6 0

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.

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