Answer:
117,600 ways
Step-by-step explanation:
This problem can be solved using fundamental principle of counting , according to which , if there are m different things and n different things,
then there m*n ways to combine.
Example: if there 5 shirts and 3 ties,
then number of ways in which different combination shirt and tie can be worn is
5*3 = 15 ways.
____________________________________
In the problem,\
number of states is 50,
let those states be
A1, A2, A3, A4 ......A50
in each state there are 2 senate
Condition
3-Senator committee in which no two members are from the same state.
then
first member can be chosen from any of the 50 state,
hence first member can be chosen in 50 ways
for simplicity lets take state A1, you can choose any one you wish
second member cannot be from state A1, then number of state left = 49
second member can be chosen from any of 49 state left
hence second member can be chosen in 49 ways
for simplicity lets take state A2,
Third member cannot be from state A1 and A2, then number of state left = 48
Third member can be chosen from any of 48 state left
hence Third member can be chosen in 48 ways
for simplicity lets take state A3,
Hence no. of ways of choosing 3-Senator committee be formed such that no two Senators are from the same state = 50*49*48 = 117,600 ways
( parellel lines have the same slope)