Question

Help please on solving this, here is the problem https://vie1160-912-pps.gradpoint.com/Resource/8766464,0/Assets/testitemimages/algebra_1b/rational_equations/al1combi-mc001-1.jpg (it might show up very small in the top corner)

Here are the possible answers:

A. 210
B. 1
C. 5,040
D. 35

Answer 1

\(_7 C _3\) is the number of 3-member groups you can make from a 7-member sets, where order doesn't matter. I read it as "7 choose 3".
The formula for combinations is:
\[_n C _r = \frac{n!}{r!(n-r)!}\]

Answer 2

oh wow i see thank you very much for the formula, I am still not sure at all how to solve it tho. It looks like a very confusing problem :/

Answer 3

Do you know what a factorial is?

Answer 4

just looked it up, now i know what it is but wow....its confusing, so sorry iv just never solved a problem like that before

Answer 5

A factorial is a number multiplied by all the numbers less than it. For example, 7! is 7 x 6 x 5 x 4 x 3 x 2 x 1

Answer 6

ohhh, now i see something familiar haha, i didn't know that 7! equaled that

Answer 7

Is it possible by chance that you can lead me through that problem if you have the time?

Answer 8

Sure!
So let's go back to the formula we had before: _n C _r = \frac{n!}{r!(n-r)!}
We have \(_7 C _3\), so n = 7 and r = 3.

Answer 9

Sorry...formula didn't work out...\[_n C _r = \frac{n!}{r!(n-r)!}\]

Answer 10

thank you :D your a lifesaver right now haha! May i ask what this equation is _n C _r = \frac{n!}{r!(n-r)!}?

Answer 11

oh, okay

Answer 12

now, if we plug in what we have for n and r:
\[_7 C _3= \frac{7!}{3!(7-3)!} = \frac{7!}{3! \cdot 4!}\]

Answer 13

If we expand the factorials, we get this:
\[\frac{7 \cdot 6 \cdot 5 \cdot 4 \cdot 3 \cdot 2 \cdot 1}{(3 \cdot 2 \cdot 1) \cdot (4 \cdot 3 \cdot 2 \cdot 1)}\]

Answer 14

and if you want to check your work, here's a handy "combination calculator"
http://www.1728.org/combinat.htm

Answer 15

oh so now i multiply all that?

Answer 16

Yep. You can cancel out some common factors between the numerator and the denominator, so you get \[\frac{7 \cdot 6 \cdot 5}{3 \cdot 2 \cdot 1}\]

Answer 17

210/6

Answer 18

Which simplifies to...?

Answer 19

35

Answer 20

That's right! Good work.

Answer 21

thank you for your help! :D

Answer 22

do you by chance have time on your hand right now?

Answer 23

My pleasure! And yes, I do. Post another question and I can help you there.