18 mice were placed in two experimental groups andone control group with all group equally large. Inhow many ways can the mice be placed into threegroups?
Answers
17153136 ways mice can be placed into three groups out of 18 mice placed with all group equally large
Step-by-step explanation:
The groups are equally large hence each group can have = 18/3 = 6 mice
The total no of ways in which the mice can be placed =18!
The possible no of ways the mice can be placed in each group = 6!
Hence the total no of ways in which the mice can be placed into three groups are = 18! / (6!×6!×6!)
= 17153136
Another ways
6 Mice for Control group can be selected in
¹⁸C₆ ways
6 mice for one Experimental group can be selected in
¹²C₆ ways
6 mice for second Experimental group can be selected in
⁶C₆ ways
= ¹⁸C₆ * ¹²C₆ * ⁶C₆
= 18! / (6!×6!×6!)
= 17153136
if both experimental group are identical
then 17153136/2!
= 85,76,568
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