Evaluate the expression 5C2?

2 Answers
Evan
May 29, 2018

#C_2^5#

#=(5!)/(2!(5-2)!)#

#=(5!)/(2!3!)#

#=10#

Explanation:

Combination formula is denoted by:

#C_r^n=(n!)/(r!(n-r)!#

Just substitute in #r=2# and #n=5#,

#C_2^5=10#

This can also be seen from Pascal's triangle where,

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Jim G.
May 29, 2018

#10#

Explanation:

#"using the definition of " ^nC_r#

#•color(white)(x) ^nC_r=(n!)/(r!(n-r)!)#

#"where "n! =n(n-1)(n-2)... xx3xx2xx1#

#"here "n=5" and "r=2#

#=(5!)/(2!xx3!)#

#color(white)(x)^5C_2=(5xxcancel(4)^2xxcancel(3)xxcancel(color(red)(2xx1)))/(cancel(color(red)(2xx1))xxcancel(3)xxcancel(2)^1xx1)=5xx2=10#

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