Combinations problem

Question

Hi Everyone! I'm new to the club. If anyone can assist me with this problem, I would be very appreciated

The topic is about Combination. Why is that 10C4 = 10C6? I understand that if we select a group of r from a pool event, we automatically create another group of (n-r) folks who were left behind. So every group of 4 corresponds to a group of 6. But if we calculate it, 10C4 = 10*9*8*7/4*3*2*1. On the other hand, 10C6 = 10*9*8*7/6*5*4*3*2*1. How is this equal to 10C4? Can someone please clarify? Thank you

chetan2u · Answer

10C4= \frac{10!}{4!(10-4)!}=\frac{10!}{4!6!} 
10C6= \frac{10!}{6!(10-6)!}=\frac{10!}{6!4!} 
so 10C4=10C6.

In your example
10C4 = 10*9*8*7/4*3*2*1. On the other hand, 10C6 = 10*9*8*7 *6*5 /6*5*4*3*2*1=10*9*8*7/4*3*2*1

ramlala · Answer

Hi  Angiee1112

In your doubt  10C6 = \frac{10*9*8*7}{6*5*4*3*2*1}  is not correct.

10C6 = \frac{10!}{6!*4!}

10C6 = \frac{10*9*6*7*6!}{6!*4*3*2*1}

10C6 = \frac{10*9*6*7}{4*3*2*1} = 10C4

s1804singh · Answer

Hi Angiee1112,

Using the Formula: nCr = n!/

Hence,
10C4 = 10! /   = 10! /

10C6 = 10!/   = 10! /   = 10! /

chocokitty · Answer

Got it, thank you 😊

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Combinations problem

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