Final answer:
There are 4 men wearing blue shirts in the room, calculated by subtracting the number of men wearing red and green shirts from the total number of men.
Step-by-step explanation:
To work out the number of men wearing a blue shirt, we start with the total number of men in the room, which is 24. Half of them wear red shirts and one-third wear green shirts. To find the number wearing red shirts, we calculate 1/2 of 24, which is 12. To find the number wearing green shirts, we calculate 1/3 of 24, which is 8. To find the number wearing blue shirts, we subtract the number of men wearing red and green shirts from the total:
Total men in room = 24
Men wearing red shirts = 24 * (1/2) = 12
Men wearing green shirts = 24 * (1/3) = 8
Men wearing blue shirts = Total - Red shirted men - Green shirted men
Men wearing blue shirts = 24 - 12 - 8 = 4.
Therefore, there are 4 men wearing blue shirts.