Questions on Algebra: Combinatorics and Permutations answered by real tutors!

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Question 162961: can someone please help me with this problem:
12C0 (the 0 is at the bottom of C)
a. 12
b. 11
c. 39,916,800
d. 1: can someone please help me with this problem:
12C0 (the 0 is at the bottom of C)
a. 12
b. 11
c. 39,916,800
d. 1
Answer by jim_thompson5910(9929) About Me  (Show Source):
You can put this solution on YOUR website!
n!/(n-r)!r! Start with the given formula



12!/(12-0)!0! Plug in n=12 and r=0



12!/12!0! Subtract 12-0 to get 12


Expand 12!
(12*11*10*9*8*7*6*5*4*3*2*1)/((12*11*10*9*8*7*6*5*4*3*2*1)0!)



(cross(12*11*10*9*8*7*6*5*4*3*2*1))/(cross(12*11*10*9*8*7*6*5*4*3*2*1))0! Cancel out the common terms



(1)/0! Simplify


Expand 0! Note: by definition 0!=1

(1)/(1)



1 Reduce


So the answer is d) 1


Think of it this way: how many ways can you assemble a team of 0 people if you have 12 people to choose from (order does not matter)? The answer is 1 since there is only one way to do this.