this question asked in gate 2017 :iit roorkee (EC,BT,PI IN SET -1)

Question

there are 3 Indians and 3 Chinese in a group of 6 people .how many subgroups of this group can we choose so that every subgroup has at least one Indian?

please help me out in this question also explain how to handle atleast case

Answer 1

1.) group with one Indian  – 3C1(choose 1 Indian out of three) * 2^3 (for Chinese people, each Chinese have 2 possibility either he present in group or not) = 3 * 2^3 =  24

2.) group with 2 Indian = 3C2 * 2^3 = 24

3.) group with 3 Indian 3C3 * 2^3 = 8

total group with at least one Indian   = 24 + 24 + 8 = 56

OR

Total Group  – group without Indian

(2^6 – 1) – (2^3) = 56

Comments

thanku