Question

How many different choices can be made from 5 roses, 4 marigold and 8 sunflowers if at least one flower is to be chosen for making of garland?

(a) 269

(b) 270

(c) 281

(d) 320

The question was posed to me in my homework.

Enquiry is from Counting in division Counting of Discrete Mathematics

Answer 1

Correct choice is (a) 269

To elaborate: Number of ways of selecting roses = (5+1) = 6 ways, number of ways of selecting marigold = (4+1) = 5 ways, and the number of ways of selecting sunflowers = (8+1) = 9 ways. Total number of ways of selecting flowers= 6 * 5 * 9 = 270. But this includes when no flowers or zero flowers is selected (There is no flowers of a different type, hence n=0 =>   2^n  = 2^0 = 1). Hence, the number of ways of selecting at least one fruit = 270 – 1 = 269.