What are the uses of pascal's triangle in real life?

Taniyah Estrada
2022-06-27
Answered

What are the uses of pascal's triangle in real life?

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asked 2021-09-09

In a fuel economy study, each of 3 race cars is tested using 5 different brands of gasoline at 7 test sites located in different regions of the country. If 2 drivers are used in the study, and test runs are made once under each distinct set of conditions, how many test runs are needed?

asked 2021-09-08

A restaurant offers a $12 dinner special that has 7 choices for an appetizer, 12 choices for an entree, and 6 choices for a dessert. How many different meals are available when you select an appetizer, an entree,and a dessert?

asked 2022-08-09

There are 8 area code numbers in the Boston area $(351,978,617,857,339,781,508,774)$. If a telephone number is chosen at random explain why the probability of if the number to start with 617 is not 1/8.

asked 2022-05-28

There are three colors of counter, red, green and blue.

There are 5 red, 3 green and 2 blue counters already in the bag.

Another counter is added to the bag (completely randomly).

A counter is chosen from the bag.

Given that the counter chosen is green, what's the probability that the counter added to the bag was green?

There are 5 red, 3 green and 2 blue counters already in the bag.

Another counter is added to the bag (completely randomly).

A counter is chosen from the bag.

Given that the counter chosen is green, what's the probability that the counter added to the bag was green?

asked 2022-05-27

Prove that $(}\genfrac{}{}{0ex}{}{2n}{n}{\textstyle )}=\sum _{k=0}^{n}{{\textstyle (}\genfrac{}{}{0ex}{}{n}{k}{\textstyle )}}^{2$

So far I have tried writing the right hand side in different ways: expressing it in its factorial form and have tried to implement the identity

$(}\genfrac{}{}{0ex}{}{n}{k}{\textstyle )}={\textstyle (}\genfrac{}{}{0ex}{}{n-1}{k-1}{\textstyle )}+{\textstyle (}\genfrac{}{}{0ex}{}{n-1}{k}{\textstyle )$

but have not gained any new ground. If any one has an algebraic proof, or even a simple combinatorics proof that is intuitive and used with an example that would be preferable.

So far I have tried writing the right hand side in different ways: expressing it in its factorial form and have tried to implement the identity

$(}\genfrac{}{}{0ex}{}{n}{k}{\textstyle )}={\textstyle (}\genfrac{}{}{0ex}{}{n-1}{k-1}{\textstyle )}+{\textstyle (}\genfrac{}{}{0ex}{}{n-1}{k}{\textstyle )$

but have not gained any new ground. If any one has an algebraic proof, or even a simple combinatorics proof that is intuitive and used with an example that would be preferable.

asked 2022-05-29

Suppose $S\subset \mathbb{Z}$ (set of integers) such that

1) $|S|=15$

2) $\mathrm{\forall}\text{}s\in S,\mathrm{\exists}\text{}a,b\in S$ such that $s=a+b$

Show that for every such $S$, there is a non-empty subset $T$ of $S$ such that the sum of elements of $T$ is zero and $|T|\le 7$.

1) $|S|=15$

2) $\mathrm{\forall}\text{}s\in S,\mathrm{\exists}\text{}a,b\in S$ such that $s=a+b$

Show that for every such $S$, there is a non-empty subset $T$ of $S$ such that the sum of elements of $T$ is zero and $|T|\le 7$.

asked 2021-05-26

In how many ways can a 10-question true-false exam be answered? (Assume that no questions are omitted)