How do you evaluate 9C3?

2 Answers
Oct 27, 2017

Answer:

#84#

Explanation:

in general

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

#color(white)(x)^9C_3=(9!) /(3!(9-3)!#

#=(9!)/(3!6!)#

#=(9xx8xx7xxcancel(6!))/ (3!cancel(6!)#

#=(cancel(9)^3xxcancel(8)^4xx7)/(cancel(3)xxcancel(2)xx1)#

#=3xx4xx7=84#

Oct 27, 2017

Answer:

#84#

See steps below;

Explanation:

#"Formular" rArr ^nC_r = (n!)/((n - r)! r!)#

Where.... #c = 9, r = 3#

#rArr ^9C_3 = (9!)/((9 - 3)!3!)#

#color(white)(xxxx) rArr (9!)/((9 - 3)!3!)#

#color(white)(xxxx) rArr (9!)/((6)!3!)#

#color(white)(xxxx) rArr (9!)/(6!3!)#

#color(white)(xxxx) rArr (9 xx 8 xx 7 xx 6 xx 5 xx 4 xx 3 xx 2 xx 1)/((6 xx 5 xx 4 xx 3 xx 2 xx 1) (3 xx 2 xx 1))#

#color(white)(xxxx) rArr (9 xx 8 xx 7 xx cancel6 xx cancel5 xx cancel4 xx cancel3 xx cancel2 xx cancel1)/((cancel6 xx cancel5 xx cancel4 xx cancel3 xx cancel2 xx cancel1) (3 xx 2 xx 1))#

#color(white)(xxxx) rArr (9 xx 8 xx 7)/(3 xx 2 xx 1)#

#color(white)(xxxx) rArr 504/6#

#color(white)(xxxx) rArr 84#