Answer:
[tex]_{3}C_{2}[/tex] = 3; [tex]_{3}C_{3}[/tex] = 1
Step-by-step explanation:
You can start by substituting the values of n and r into the basic formula:
[tex]_{n}C_{r}[/tex] = [tex]\frac{n!}{(n - r)!r!}[/tex]
[tex]_{3}C_{2}[/tex] = [tex]\frac{3!}{(3 - 2)! * 2!}[/tex]
Now, simplify the numerator and the denominator:
[tex]\frac{3!}{(3 - 2)! * 2!}[/tex] = [tex]\frac{6}{1 * 2}[/tex] = 3
[tex]_{3}C_{2}[/tex] = 3
For the second instance, do the same thing:
[tex]_{n}C_{r}[/tex] = [tex]\frac{n!}{(n - r)!r!}[/tex]
[tex]_{3}C_{3}[/tex] = [tex]\frac{3!}{(3-3)!*3!}[/tex]
Finally, simplify the numerator and denominator:
[tex]\frac{3!}{(3-3)!*3!}[/tex] = [tex]\frac{6}{6}[/tex] = 1
[tex]_{3}C_{3}[/tex] = 1
