Question

There are 16 people, they divide into four equal groups, now from those four groups select a team of three members,such that no two members in the team should belong to same group.

Answer 1

Total number of team can be formed like this

A B C OR A B D OR A C D OR B C D .

So for first team 1 member selected from group A by 4c1 ways ,

Similarly 1 member from B by 4c1 ways ,

Similarly from C by 4c1 ways.

So we can select 1st team by 4c1 * 4c1 *4c1 *4c1  

Since we can select team as ABC OR ABD OR ACD OR BCD

So no of ways of selecting team is

(4c1 * 4c1 *4c1 *4c1 ) OR (4c1 * 4c1 *4c1 *4c1 ) or (4c1 * 4c1 *4c1 *4c1 ) OR (4c1 * 4c1 *4c1 *4c1 )=

(4c1 * 4c1 *4c1 *4c1 ) + (4c1 * 4c1 *4c1 *4c1 ) + (4c1 * 4c1 *4c1 *4c1 ) + (4c1 * 4c1 *4c1 *4c1 ) =  

64+64+64+64

= 256