Answer:
35
Step-by-step explanation:
Using the definition of n[tex]C_{r}[/tex]
with n = 7 and r = 3
7[tex]C_{3}[/tex]
= [tex]\frac{7!}{(7-3)!3!}[/tex]
= [tex]\frac{7!}{4!(3!)}[/tex]
= [tex]\frac{7(6)(5)(4)(3)(2)(1)}{4(3)(2)(1)3(2)(1)\\}[/tex] ← cancel 4(3)(2)(1) on numerator/denominator
= [tex]\frac{7(6))(5)}{3)2)(1)}[/tex]
= [tex]\frac{210}{6}[/tex]
= 35
