Question

QUESTION 1 47% of Americans like brocolli, 63% of Americans like cauliflower, and 28% of Americans like both brocolli and cauliflower. What percentage of Americans like neither vegetable? QUESTION 2 Simplify C(n,r)+2C(n,r-1)+C(n,r-2) (Hint: split the middle term)

Answer 1

1. Given That 474) of Americans like brocolli[n[1]]= 047 63% of Amenicons like Cauliflower Cnces]=0.63 and 28% of Americans lace both brocolli and Cauliflower (nebnc)] -0.28 therefore , we use principle of melusion-ea Clusion. n(buc) = n(b) = n(A) = n(bre) 6. 47+0.63 -0.28 = 0.82 thus, the ston percentage of Americans live neither vegetables 21-082 20.18.0 18 % therefore, 18% of Americans lite neither vegetawei

Given that 2 ccnir) 42 0(0,01) + C(DV-2) we know that northery=ntier, and Chir) = nor. ccnir) +2 C (nor-1) + C (nor-2) Now, consider = ner 42 neras & ner-2 (naher nera neras thery of neraz it (+1) Carl (012). ccnt2,8) therefore, e(n,r) 42C(n,r-1) + C (214-2)= C(nazir).
Quastion 1: 18%

Quastion 2: C(n+2,r)