Coin Pnc
A man has 3 pocket and 4 coins. In how many ways can he put the coins in his pocket? DOUBT?
ANS: First coin can be put in 3 ways, similarly second, third and fourth coins also can be put in 3 ways. So, 3*3*3*3.
I m confused as: why not 4*4*4? 1st pocket can have 4 coins..??[confused]?
please answer explaining basic concept of PnC. Thanks.
i know that answer is 3*3*3*3. But, why cant 4*4*4 be applied? I know that HERE applying 4*4*4 seems illogical. But in general, in situations which should be applied? i want the concept explained fully.
If you are thinking in terms of pockets, it will complicate the matters.
In case of coins, where you keep one coin will not affect where you keep the next coin.
But if you think in terms pockets, how many coins you keep in one pocket, will affect how many coins can be put in other pockets.
Let us see.
Consider pocket A :
Here you can keep either 0 coins or 1 coin or 2 coins or 3 coins or 4 coins. (That makes it five — not the four possibilities which you have wrongly thought of)
In case of 0 coins, the second pocket can have 0 coins or 1 coin or 2 coins or 3 coins or 4 coins … and then we have to think of third pocket also as sub cases….
In case of 1 coin, the second pocket can have 0 coins or 1 coin or 2 coins or 3 coins….. and then sub cases etc.
Let us simplify: The possible arrangements of combinations are
A B C No. of comibations
0 0 4 1
0 1 3 4
0 2 2 6
0 3 1 4
0 4 0 1
1 0 3 4
1 1 2 12
1 2 1 12
1 3 0 4
2 0 2 6
2 1 1 12
2 2 0 6
3 0 1 4
3 1 0 4
4 0 0 1
Total 81 possiblilities.
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