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Masja [62]
4 years ago
14

How many combinations of four books can be made from eight different books? 24 70 1,680?

Mathematics
1 answer:
djverab [1.8K]4 years ago
3 0

Answer:

70

Step-by-step explanation:

four books can be made from eight different books

4 books to be chosen from 8 books

The order does not matters so we use Combination.

four books can be made from eight different books, so we find 8C4

nCr= \frac{n!}{r!(n-r)!}

8C4= \frac{8!}{4!(8-4)!}

8C4= \frac{8!}{4!(4)!}

8C4= \frac{8*7*6*5*4!}{4!(4)!}=70

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<h3>Answer: Choice B</h3>

Use a rigid transformation to prove that angle NPO is congruent to angle NLM

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Explanation:

The AA stands for "angle angle". So we need two pairs of angles to prove the triangles to be similar. The first pair of angles is the vertical angles ONP and MNL, which are congruent. Any pair of vertical angles are always congruent.

The second pair of angles could either be

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so we have a choice on which to pick. The pairing angle NOP = angle NML is not listed in the answer choices, but angle NPO = angle NLM is listed as choice B.

Saying angle NLM = angle LMN is not useful because those two angles are part of the same triangle. The two angles must be in separate triangles to be able to tie the triangles together.

We would use a rigid transformation to have angle NPO move to angle NLM, or vice versa through the use of a rotation and a translation.

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