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SCORPION-xisa [38]
3 years ago
6

six runners are entered in a race.Assume there are no ties In how many ways can first and second place be awarded

Mathematics
1 answer:
cluponka [151]3 years ago
7 0
P(6,2) = 6!/(6-2)!
P(6,2) = 6!/4! 6! = 1*2*3*4*5*6 4! = 1*2*3*4
P(6,2) = (1*2*3*4*5*6)/(1*2*3*4)
P(6,2) = (5*6)/1
P(6,2) = 30
I hope this makes sense. Let me know if you don't understand any of this. ☺♥

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Zarrin [17]

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\dfrac{9}{2}

Step-by-step explanation:

You can do this using the quadratic equation:

x =\dfrac{-b\pm\sqrt{b^{2}-4ac}}{2a}

Let's first setup our expression:

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Now we plug in our coefficients and solve:

x =\dfrac{-12\pm\sqrt{12^{2}-4(4)(-135)}}{2(4)}

We solve for both to determine the positive one:

x =\dfrac{-12+ \sqrt{12^{2}-4(4)(-135)}}{2(4)}              x =\dfrac{-12- \sqrt{12^{2}-4(4)(-135)}}{2(4)}

x =\dfrac{-12+ \sqrt{144+2160}}{8}                        x =\dfrac{-12- \sqrt{144+2160}}{8}

x =\dfrac{-12+ \sqrt{2304}}{8}                                 x =\dfrac{-12- \sqrt{2304}}{8}

x =\dfrac{-12+ 48}{8}                                        x =\dfrac{-12- 48}{8}

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So if you are looking for a positive solution, just take the positive one as x.

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Hope this helps!! Have a great day!! :)))
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