IN HOW MANY WAYS, WE CAN CHOOSE TWO TEAMS OF MIXED DOUBLE FOR A TENNIS TOURNAMENT FROM FOUR COUPLES SUCH THAT IF ANY COUPLE PARTICIPATES,THEN IT IS IN THE SAME TEAM
Answers
42 Teams can be selected
Step-by-step explanation:
M1 M2 M3 M4
F1 F2 F3 F4
2 Males can be selected in ⁴C₂ - 6 ways
2 Females can be selected in ⁴C₂ - 6 ways
Total ways = 6 * 6 = 36
Lets Take all the case
M1 M2 F1 F2 then Possible team 1
M1 M2 F1 F3 then Possible team 1
M1 M2 F1 F4 then Possible team 1
M1 M2 F2 F3 then Possible team 1
M1 M2 F2 F4 then Possible team 1
M1 M2 F3 F4 then Possible team 2
M1 M3 F1 F2 then Possible team 1
M1 M3 F1 F3 then Possible team 1
M1 M3 F1 F4 then Possible team 1
M1 M3 F2 F3 then Possible team 1
M1 M3 F2 F4 then Possible team 2
M1 M3 F3 F4 then Possible team 1
M1 M4 F1 F2 then Possible team 1 -
M1 M4 F1 F3 then Possible team 1 -
M1 M4 F1 F4 then Possible team 1
M1 M4 F2 F3 then Possible team 2
M1 M4 F2 F4 then Possible team 1
M1 M4 F3 F4 then Possible team 1
M2 M3 F1 F2 then Possible team 1
M2 M3 F1 F3 then Possible team 1
M2 M3 F1 F4 then Possible team 2
M2 M3 F2 F3 then Possible team 1
M2 M3 F2 F4 then Possible team 1
M2 M3 F3 F4 then Possible team 1
M2 M4 F1 F2 then Possible team 1
M2 M4 F1 F3 then Possible team 2
M2 M4 F1 F4 then Possible team 1
M2 M4 F2 F3 then Possible team 1
M2 M4 F2 F4 then Possible team 1
M2 M4 F3 F4 then Possible team 1
M3 M4 F1 F2 then Possible team 2
M3 M4 F1 F3 then Possible team 1
M3 M4 F1 F4 then Possible team 1
M3 M4 F2 F3 then Possible team 1
M3 M4 F2 F4 then Possible team 1
M3 M4 F3 F4 then Possible team 1
Total Possible teams = 6 * 7 = 42
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