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2 years ago

We form a committee of 8 people, to be chosen from 15 women and 12 men. (a) How many possible committee can be formed

Mathematics

1 answer:

eimsori [14]2 years ago

3 0

Using the combination formula, it is found that 2,220,075 committees can be formed.

The order in which the people are chosen is not important, hence, the <em>combination formula</em> is used to solve this question.

<h3>Combination formula: </h3>

$C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by:

$C_{n,x} = \frac{n!}{x!(n-x)!}$

In this problem, 8 people are chosen from a set of 12 + 15 = 27, hence:

$C_{27,8} = \frac{27!}{8!19!} = 2220075$

2,220,075 committees can be formed.

To learn more about the combination formula, you can take a look at brainly.com/question/25821700

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Triangles XQP and YRS are right triangles because triples 6, 8, 10 are Pythagorean triples.

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all angles of the quadrilateral XAYB are right angles

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Read 2 more answers

Felicity's dog eats no more than two cups of dog food per day. Felicity's dog eats at least one-quarter cup more than one-half o

horrorfan [7]

Answer:

$\frac{1}{4}+\frac{m}{2} \leq x\leq 2$

$x$ denotes amount of food that Felicity's dog eats

Step-by-step explanation:

Given:

Felicity's dog eats no more than two cups of dog food per day.

Felicity's dog eats at least one-quarter cup more than one-half of the amount Martin's dog eats.

The amount of food that Martin's dog eats is represented by using $m$

To find: the inequality that represents the situation

Solution:

Amount of food that Martin's dog eats = $m$

Amount of food that Felicity's dog eats ≤ 2

Also,

Amount of food that Felicity's dog eats $\geq \frac{1}{4}+\frac{m}{2}$

Therefore,

$\frac{1}{4}+\frac{m}{2}\leq$ Amount of food that Felicity's dog eats ≤ 2

Let $x$ denotes amount of food that Felicity's dog eats.

$\frac{1}{4}+\frac{m}{2}$ ≤ $\frac{1}{4}+\frac{m}{2} \leq x\leq 2$

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