A closed wooden box has holes of diameter 3, 5, 5, and 6 cm drilled into lid. 4 coins of diameter 2, 4, 5and 6 cm are to be placed in box. Determine how may ways this can be done if
i) 1 coin must be inserted through each hole
ii) no such restruction is made
Originally posted by quailmaster:A closed wooden box has holes of diameter 3, 5, 5, and 6 cm drilled into lid. 4 coins of diameter 2, 4, 5and 6 cm are to be placed in box. Determine how may ways this can be done if
i) 1 coin must be inserted through each hole
ii) no such restruction is made
For i),
The 6 cm diameter coin must go through the 6cm diameter hole, no doubt. Similarly, the 2 cm diameter coin must go through the 3 cm diameter hole, since no other coins can fit through it. Thus, we are left with only 2 choices.
For ii),
The 6cm diameter coin is still stuck with the 6cm diameter hole. Now, let us have a look at the other coins. For the 2cm diameter coin, we have 4 options, whereas the 4cm diameter and 5cm diameter coins each have 3 options since neither can enter the 2 cm diameter hole.
Hence, we have 4 X 3 X 3 = 36 ways.
For part ii shouldn't it be 4!+1?
4! is when you arrange the coins without considering the holes and then those that can't fit = empty hole
+1 is when none of the slots are used
Originally posted by TenSaru:For part ii shouldn't it be 4!+1?
4! is when you arrange the coins without considering the holes and then those that can't fit = empty hole
+1 is when none of the slots are used
No, the coins must go into the box.
ok