likithae wrote:

Four boys picked up 30 mangoes .In how many ways can they divide them if all mangoes be identical?

help me to solve .........

1. If boys can get zero mangoes them the answer would be - (30+4-1)C(4-1)=33C3:Consider 30 Mangoes: ****************************** and 3 separators |||.

Permutations of these 33 symbols out of which 30 *'s and 3 |'s are identical is

\frac{33!}{3!30!}, or written in another way

C^3_{33}.

Each permutation will mean one particular distribution of 30 mangoes among 4 boys:

******************************||| first boy gets all mangoes;

*|*|*|*************************** first, second and third boys get 1 mango each, and fourth gets 27;

*||*|*************************** first gets one mango, second boy gets zero, third boy get 1 and fourth gets 28;

And so on.

2. If boys should get at least one mango then the answer would be - (26+4-1)C(4-1)=29C3 (basically we are distributing 26 mangoes):The same as above: we should jut give 1 mango to each boy and then distribute 26 mangoes left as in previous case.

26 Mangoes: ************************** and 3 separators |||.

Permutations of these 29 symbols out of which 26 *'s and 3 |'s are identical is

\frac{29!}{3!26!}, or written in another way

C^3_{29}.

Again each permutation will mean one particular distribution of 26 mangoes among 4 boys.

Similar problems:

voucher-98225.html?hilit=separatorsintegers-less-than-85291.html?hilit=identical#p710836Direct formula:

The total number of ways of dividing n identical items among r persons, each one of whom, can receive 0,1,2 or more items is n+r-1C_{r-1}.

The total number of ways of dividing n identical items among r persons, each one of whom receives at least one item is n-1C_{r-1}.P.S. 4^30 would be the answer if all mangoes were different but we are told that they are identical.

Hope it helps.

used for number of ways of dividing n identical items among r persons whom can receive

. Are you saying the same formula is used even if each person can receive 2 or 3 or anyitem? Why isn't that being factored in to the formula?

How many ways are there to distribute 10 mangoes among 4 kids if each kid must receive

How many ways are there to distribute 10 mangoes among 4 kids if each kid must receive

How many ways are there to distribute 10 mangoes among 4 kids if each kid must receive

Are you saying this formula gives us the same answer for all these questions? (10+4-1)C(4-1)?