How do you evaluate #""""_7C_4#?

1 Answer
Jul 3, 2017

Answer:

# ""^7C_4 = 35 #

Explanation:

We evaluate combinations using definition:

# ""^nC_r = ( (n), (r) ) = (n!)/( (n-r)! \ r!) #

Thus:

# ""^7C_4 = (7!)/( (7-4)! \ 4!) #
# " " = (7!)/( 3! \ 4!) #
# " " = (1.2.3.4.5.6.7)/( (1.2.3) \ (1.2.3.4)) #
# " " = (5.6.7)/( (1.2.3) ) #
# " " = (5.7) #
# " " = 35 #

Or we could evaluate by just comoputing thefactorial values

# ""^7C_4 = = (7!)/( 3! \ 4!) #
# " " = (5040)/( 6 * 24) #
# " " = (5040)/( 144) #
# " " = 35 #

Finally, most modern calculators have the ability to peform combination calculations via an #nCr# or # ""^nC_r # button