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.