How many different ways can 25 students line up for lunch?

Mathematics

2 answers:

zheka24 [161]3 years ago

7 0

$25!=15,511,210,043,330,985,984,000,000$

aivan3 [116]3 years ago

6 0

Answer:

$25!=15511210043330985984000000$

Step-by-step explanation:

We are asked to find the number of ways 25 students line up for lunch.

Since there are 25 students, so the students for the 1st place can be chosen in 25 ways.

As 1 student is already chosen for 1st place and there are 24 students left, so the students for the 2nd place can be chosen in 24 ways.

Since 2 students are already chosen and there are 23 students left, so the students for the 3rd place can be chosen in 23 ways.

We will continue this process till we fill all the 25 places.

$\text{The number of ways to line up for lunch}=25*24*23*22*21*20*19*.......*1$

We can represent $25*24*23*22*21*20*19*.......*1$ as $25!$ , therefore, 25 students can be line up for lunch in $25!=15511210043330985984000000$ different ways.

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LabTech is a company that manufactures microscopes and other laboratory instruments . On occasion, one of the microscopes is def

Scrat [10]

Answer:

0.0782 (7.82%)

Step-by-step explanation:

The required probability will be found by using the Binomial Distribution which fits the case of n independent events each with a probability of success equal to p with k successes.

The PMF (Probability Mass Function) is

$f(k,n,p)=\binom{n}{k}p^kq^{n-k}$

Where $q = 1-p$

LabTech states that the probability that a microscope is defective is 0.17%, p=0.0017, q=0.9983. We need to know the probability that k=1 microscope is defective out of a set of n=50 of them. We now apply the formula

$f(1,50,0.0017)=\binom{50}{1}0.0017^10.9983^{49}=0,0782$