### Vocabulary

##### Complete the chart.

Word | Definition |

Combination | ____________________________________________________________ |

Factorial | ____________________________________________________________ |

Binomial Theorem | ____________________________________________________________ |

_______________ | the process of raising a binomial such as (x + 2) to a power |

_______________ | a pyramid of sorts constructed with the coefficients of binomials as they are expanded |

### Factorials and Combinations

Expand ___________________________________

**Simplify and Evaluate the Factorials:**

**Solve**

- The local TV station forecasts a 14% chance of rain every day for the next week. What is the probability that it will rain on exactly 4 out of the next 7 days?

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#### Binomial Theorem and Expansions

Pascal's Triangle can help expand binomials.

It follows the pattern .

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When you expand ( x + y )^{ n} , the exponents of *x ______________ *whille the exponents of *y* ______________.

What is the Binomial Theorem in summation form? _________________________

Explain how finding a term in an expansion can be used to answer a particular kind of probability question. _____________________________________________________________________________________________________________________________________________

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- Expand:
- Expand:
- Expand:
- Find the 5th term in the expansion .
- What is the coefficient of in the expansion of ?

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