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Alina [70]
3 years ago
7

In a race between 18 people, how many ways can the top 5 finishers be arranged?

Mathematics
1 answer:
snow_lady [41]3 years ago
8 0

Answer:

Step-by-step explanation:

This is permutation, since order matters.  The formula for us is

₁₈P₅ = \frac{18!}{(18-5)!} which simplifies to

₁₈P₅ = \frac{18*17*16*15*14*13!}{13!}

The factorial of 13 cancels out on the top and bottom leaving you with

₁₈P₅ = 18 × 17 × 16 × 15 × 14

which comes to 1,028,160 ways

Another way to look at it is:  the first 5 people of 18 finish and the others you don't care about.  Once the first place person is first, there are only 4 of the 18 left to finish in second place.  Then there are only 3 left to finish in third place, etc.  So if we use that reasoning, we don't even need to use the formula, we can just say

18 * 17 * 16 * 15 * 14 and those are the first 5 people of 18 to finish.

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3 years ago
How do i calculate? All the way to s_75. It’s so long
mina [271]

Answer:

  -675

Step-by-step explanation:

The sum can be broken into parts that you know. Here, one of those parts is the sum of numbers 1 to n. That sum is given by n(n+1)/2.

\displaystyle S_{75}=\sum\limits_{n=1}^{75}{(67-2n)}=\sum\limits_{n=1}^{75}{67}-2\sum\limits_{n=1}^{75}{n}\\\\=75\cdot 67-2\dfrac{75(75+1)}{2}=75(67-76)\\\\=\bf{-675}

__

Another way to do this is to realize the sequence of numbers is an arithmetic sequence with a first term of 65 and a last term of 67-2·75 = -83.

The sum of an arithmetic sequence is found by multiplying the number of terms by their average value. Their average value is the average of the first and last terms.

The average value of those 75 terms is (65 +(-83))/2 = -9, so their sum is ...

  75(-9) = -675

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3 years ago
Can I please get help with this?
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Answer: x = 20.

Step-by-step explanation:

x and (3x + 10) combine to form a right angle, shown in the diagram by the small square joining the perpendicular lines.

Right angles are 90 degrees, so you can add both angles to get 90:

x + (3x + 10) = 90\\\\4x + 10 = 90\\\\4x = 80\\\\x = 20

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