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Marizza181 [45]
3 years ago
9

A total of 28 students have entered a spelling contest. There are 6 medals for first through sixth place will be awarded. In how

many different ways can the medals be awarded?
A. 178,340
B. 376,740
C. 271,252,800
D. 96, 860

(I am terrible at probability questions.)
Mathematics
1 answer:
zhuklara [117]3 years ago
4 0
This is a permutation / combination problem.

For the 1st position there are 28 possibilities.

<span>For the 2nd position there will be 27 possibilities left.</span>

For the 3rd position there will be<span> 26 possibilities left</span><span>.
</span>
For the 4th position there will be 25 possibilities left<span>.
</span>
For the 5th position there will be 24 possibilities left<span>.
</span>
For the 6th position there will be 23 possibilities left<span>.
</span>
Total = 28*27*26*25*24*23 = <span>271,252,800</span>

C. 271,252,800
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Can someone please explain how the answer is D
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Step-by-step explanation:

Because the length of ST is calculated using pythagorean theorem:

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Where the square of the hypotenuse is equal to the sum of squares of the other two sides of a right triangle. In this case, the hypotenuse is ST and the other two sides are distances between S and T over the X and Y axis. Those are easily calculated:

x =  |sx - tx|  \\ y =  |sy - ty|

Where x is the distance between S and T over X axis and Y distance over Y axis, sx and tx are X coordinates of S and T, sy and ty are Y coordinates of S and T.

Using that formula, you get that y = 17 and x = 8.

Back to the pythagorean theorem, if we put those number in the formula of the pythagorean theorem, we get something like this:

{c}^{2}  =  {x}^{2}  +  {y}^{2} \\  {c}^{2}  =  {8}^{2}  +  {17}^{2} = 64 + 289  \\  {c}^{2}  = 353 \\ c =  \sqrt{353}

And finally, the correct answer is in fact 353.

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