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3 years ago

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Exercise topic: Permutations and Combinations. A company wants to hire 3 new employees, but there are 8 candidates, 6 of them wh

ich are men and 2 are women. If the selection is random: a) In how many different ways can choose new employees? b) In how many different ways can choose a single male candidate? c) In how many different ways can choose at least one male candidate? with procedures. Help me please..

1 answer:

SOVA2 [1]3 years ago

8 0

Answer:

(a) 56 ways

(b) 6 ways

(c) 56 ways

Step-by-step explanation:

Given:

candidates: 6 mail, 1 female

number to hire : 3

a) In how many different ways can choose new employees?

use the combination formula to choose r to hire out of n candidates

C(n,r) = C(8,3) = 8! / (3! (8-3)! ) = 40320 / (120*6) = 56 ways

b) In how many different ways can choose a single male candidate?

6 ways to choose a male, one way to choose two female, so 6*1 = 6 ways

c) In how many different ways can choose at least one male candidate?

To choose at least 1 male candidate, we subtract the ways to choose no male candidates out of 56.

Since there are only two females, there is no way to choose 3 female candidates.

In other words, there are 56-0 = 56 ways (as in part (a) ) to hire 3 employees with at least one male candidate.

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Using the binomial distribution, the probabilities are given as follows:

a) 0.4159 = 41.59%.

b) 0.5610 = 56.10%.

c) 0.8549 = 85.49%.

<h3>What is the binomial distribution formula?</h3>

The formula is:

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

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

The parameters are:

x is the number of successes.

n is the number of trials.

p is the probability of a success on a single trial.

For this problem, the values of the parameters are:

n = 3, p = 0.76.

Item a:

The probability is P(X = 2), hence:

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 2) = C_{3,2}.(0.76)^{2}.(0.24)^{1} = 0.4159$

Item b:

The probability is P(X < 3), hence:

P(X < 3) = 1 - P(X = 3)

In which:

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 3) = C_{3,3}.(0.76)^{3}.(0.24)^{0} = 0.4390$

Then:

P(X < 3) = 1 - P(X = 3) = 1 - 0.4390 = 0.5610 = 56.10%.

Item c:

The probability is:

$P(X \geq 2) = P(X = 2) + P(X = 3) = 0.4159 + 0.4390 = 0.8549$

More can be learned about the binomial distribution at brainly.com/question/24863377

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2 years ago

svet-max [94.6K]

Answer:

The polygon has 9 sides

Step-by-step explanation:

we know that

A regular polygon has equal length sides and equal interior angles

step 1

Find the measure of the interior angle

Remember that

The interior angle plus the exterior angle must be equal to 180 degrees (form a linear pair)

Let

x ----> the measure of each interior angle in the regular polygon

so

$x+40^o=180^o$

solve for x

$x=180^o-40^o=140^o$

step 2

Find the number of sides of the regular polygon

we know that

The measure of each interior angle in a regular polygon is given by the formula

$x=\frac{(n-2)180^o}{n}$

where

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substitute the given values

$140^o=\frac{(n-2)180^o}{n}$

solve for n

$140n=180n-360\\180n-140n=360\\40n=360\\n=9\ sides$

therefore

The polygon has 9 sides

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