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qwelly [4]
2 years ago
14

Simplify the expression 6C5. a.6. b. 24 C. 30 d. 720

Mathematics
1 answer:
Lana71 [14]2 years ago
8 0
<h3>Answer:  A) 6</h3>

=====================================================

Explanation:

Plug n = 6 and r = 5 into the nCr combination formula

_n C _r = \frac{n!}{r!*(n-r)!}\\\\_6 C _5 = \frac{6!}{5!*(6-5)!}\\\\_6 C _5 = \frac{6!}{5!*1!}\\\\_6 C _5 = \frac{6*5*4*3*2*1}{5*4*3*2*1*1}\\\\_6 C _5 = \frac{720}{120}\\\\_6 C _5 = 6\\\\

Or you could use the shortcut

_n C _{n-1} = n\\\\

Yet another path you could take is to use Pascal's Triangle. Locate the row that starts with 1,6,... and then locate the second to last item. That value in the triangle is 6.

A real world interpretation is to consider having 6 people and you are selecting 5 of them to form a group where order doesn't matter. How many ways are there to do this? Well there are 6 such ways because there are 6 ways to leave someone out of the group.

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zhuklara [117]

Answer:

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To reach her fitness goal, she needs to run for more than 8 days.

Step-by-step explanation:

She has already run 35 miles and runs 4 miles per day:

This means that after x days, the distance she will have run is:

D(x) = 35 + 4x

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This means that:

D(x) > 67

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35 + 4x > 67

Solution:

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