At Hogwarts School of Witchcraft and Wizardry, the Sorting Hat chooses one of four houses for each first-year student. If 4 students are randomly selected from 16 available students (including Harry Potter), what is the probability that they are the four youngest students?

Probability that they are the youngest is 0.000549

Step-by-step explanation:

Given

Number of students = 16

Selected students = 4

Let n = number of students

n = 16

Let r = selections

r = 4

We're interested in selecting 4 students out of 16; the keyword, selection means we're dealing with combination because order is not important.

So,

Solving for nCr

nCr = n!/((n-r)!r!)

16C4 = 16!/((16-4)!4!)

16C4 = 16!/(12!4!)

16C4 = 16 * 15 * 14 * 13 * 12!/(12!4!)

16C4 = 16 * 15 * 14 * 13 / 4 * 3 * 2 * 1

16C4 = 1820 ways

There are 1820 ways of selecting 4 students from a total of 1820.

Only one of these ways can the four of them be the youngest.

So, probability = 1/1820

Probability = 0.0005494506

Probability that they are the youngest is 0.000549 (approximately)

step-by-step explanation:

30% of $420 is 0.30($420) = $126 and $420 + $126 = $546.

or, 130% of $420 is 1.3($420) = $546.

notice that this is not the $600 original list price with which we started.

why doesn't this work?

the method does not work because 30% of $420 is not the same amount as the 30% of $600. it may seem obvious when stated this way, but it is a very common error made on problems of this type. we cannot just use the same percent and get back to the original amount because we are taking that percent of a different value.

to work problems of this type correctly, it is generally best to write an equation for the situation and then solve.

example: since (100% – 30%)(original price) = (sale price)

70% of the   (original price) is $420.

0.7x   = 420

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x = 600

the original cost was $600.

we may also solve this problem using the two-step method. working the problem in two steps requires us to use more algebra skills. we have to know that x = 1x (identity property of multiplicationtext annotation indicator) and that 1x – 0.3x = 0.7x (subtracting like terms). then we solve the problem as follows:

(original price) – 30%(original price) = sale price

x – 0.3x = 420

0.7x = $420

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x = 600

the original cost was $600.  

note that with both of the above methods we do obtain the correct original amount.

example: after a 5% pay raise, hermione is earning $22,680 per year. what was she earning before the pay raise?

105% of (original salary) = current salary

1.05x = 22,680

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x = 21,600

hermione earned $21,600 per year before the pay raise.

this is an example so maybe you will get how to at least do it!