Question

Evaluate the expression 5C2?

Answer 1

`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,

Answer 2

`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`