Answer to Question #274087 in Discrete Mathematics for Geo

Question

What are the values of the following expressions?

• ∑_(i=3)^6▒ (i^2+6)
• ∏_(j=1)^5▒ (j/2)
• 4!
• 0!
• (6¦2)
• C(6,2)

Answer 1

(i)

$$\displaystyle\sum_{i=3}^6(i^2+6)=3^2+6+4^2+6+5^2+6+6^2+6$$

$$=110$$

(ii)

$$\displaystyle\prod_{j=1}^5(i/2)=\dfrac{1(2)(3)(4)(5)}{2(2)(2)(2)(2)}=\dfrac{15}{4}$$

(iii)

$$4!=1(2)(3)(4)=24$$

(iv)

$$0!=1$$

(v)

$$P(6, 2)=\dfrac{6!}{(6-2)!}=6(5)=30$$

(vi)

$$C(6, 2)=\dfrac{6!}{2!(6-2)!}=\dfrac{6(5)}{1(2)}=15$$