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Compute \(\dbinom{14}{11}\)

 May 2, 2020

Best Answer 

 #1
avatar+652 
+1

\(\begin{align*} \dbinom{14}{11} &= \dbinom{14}{3} \\ &= \dfrac{14!}{11!3!} \\ &= \dfrac{14\times 13\times 12}{3\times 2\times 1} \\ &= 14 \times 13 \times \dfrac{12}{3\times 2\times 1} \\ &= 14\times 13\times 2 \\ &= \boxed{364}. \end{align*}\)

 

 

By the way, I wrote this even though it may look similar to ones on different websites

 

coolsmileycool

 May 2, 2020
 #1
avatar+652 
+1
Best Answer

\(\begin{align*} \dbinom{14}{11} &= \dbinom{14}{3} \\ &= \dfrac{14!}{11!3!} \\ &= \dfrac{14\times 13\times 12}{3\times 2\times 1} \\ &= 14 \times 13 \times \dfrac{12}{3\times 2\times 1} \\ &= 14\times 13\times 2 \\ &= \boxed{364}. \end{align*}\)

 

 

By the way, I wrote this even though it may look similar to ones on different websites

 

coolsmileycool

LuckyDucky May 2, 2020
 #2
avatar+189 
+1

Its correct!

SoggyPerson  May 2, 2020
 #3
avatar+652 
+1

laughlaughlaughlaughlaughlaughlaughlaughlaughlaughlaughlaughlaughlaughlaughlaughlaughlaughlaughlaughlaughlaughlaughlaughlaughlaughlaughlaughlaughlaughlaughlaughlaughlaughlaughlaughlaughlaughlaughlaughlaughlaughlaughlaughlaughlaughlaughlaughlaughlaughlaughlaughlaughlaughlaughlaughlaughlaughlaughlaughlaughlaughlaughlaughlaughlaughlaughlaughlaughlaughlaughlaughlaughlaughlaughlaughlaughlaughlaughlaughlaughlaughlaughlaughlaughlaughlaughlaughlaughlaughlaughlaughlaughlaughlaughlaughlaughlaughlaughlaughlaughlaughlaughlaughlaughlaughlaughlaughlaughlaughlaughlaughlaughlaughlaughlaughlaughlaughlaughlaughlaughlaughlaughlaughlaughlaughlaughlaughlaughlaughlaughlaughlaughlaughlaughlaughlaughlaughlaughlaughlaughlaughlaughlaughlaughlaughlaughlaughlaughlaughlaughlaughlaughlaughlaughlaughlaughlaughlaugh

 

:D

LuckyDucky  May 2, 2020
 #4
avatar+112185 
+1

Good job, LD    !!!!!

 

A "Best Answer".....

 

cool cool cool

CPhill  May 2, 2020
 #5
avatar+652 
+1

Thanks man 

 

Together we are the jam crew violin+rock

LuckyDucky  May 2, 2020
 #6
avatar+131 
+2

You got this from AoPs alcumus right? I mastered it... Anyway:

 

\(\binom{14}{11}\)= 14 x 13 x 12 x 11...3/ 11!. = 14 x 13 x 12/6 = 26 x 14 = 364

 

STOP POSTING AOPS QUESTIONS

 May 3, 2020
 #7
avatar+189 
+2

It was my last one now I will not ask anymore because I understand now for example

 

11 choose 3 = 11!/3!(11-3

= 165

SoggyPerson  May 3, 2020

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