Is #""_12C_9# greater than or less than #""_12C_7#?

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Answer 1 · 2016-05-29T14:46:44

The notation #color(white)(2)_nC_r# represents the combination formula, #(n!)/((n - r)!(r!)#. Note: #n!# is read "n factorial".

Substituting for #color(white)(2)_12C_9#, we get:

#(12!)/((12 - 9)!(9!)#

#= 220#

Substituting for #color(white)(2)_12C_7#:

#(12!)/((12 - 7)!(5!)#

#= 792#

Therefore, #color(white)(2)_12C_9 < color(white)(2)_12C_7#

Hopefully this helps!