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mathmath333
 one year ago
Counting question
mathmath333
 one year ago
Counting question

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mathmath333
 one year ago
Best ResponseYou've already chosen the best response.1\(\large \color{black}{\begin{align} \normalsize \text{In how many ways can u distribute 7 identical gifts among 5 children.}\hspace{.33em}\\~\\ \end{align}}\)

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.3say the stars are gifts : \[*~*~*~*~*~*~*\]

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.3you want to split those 7 gifts into 5 parts, so place 4 bars in between them : \[*~*~*~*~*~*~*\]

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.3that arrangement represents : 2 gifts to first child 1 gift to second child 1 gift to third child 2 gifts to fourth child 1 gift to fifth child

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.3see if you can tell what below arrangement represents : \[*~*~*~*~*~*~*\]

mathmath333
 one year ago
Best ResponseYou've already chosen the best response.11 gifts to first child 2 gift to second child 1 gift to third child 2 gifts to fourth child 1 gift to fifth child

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.3Perfect! notice, that string has 7 stars and 4 bars, so the total length of that string is 7+4 = 11

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.3as you can see, the problem translates to finding the number of ways of choosing 4 positions for the bars from the 11 positions

mathmath333
 one year ago
Best ResponseYou've already chosen the best response.1I think now the answer is 11C4. as u are seleecting 11 objects in 4 ways

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.3how many ways can you choose 4 different things(positions) from 11 different things(positions) ?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0stars and bars indeed

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.3Alternatively you could also think of it as forming different 11 letter words using 7 stars and 4 bars : 11!/(4!*7!)

mathmath333
 one year ago
Best ResponseYou've already chosen the best response.1\(\large \color{black}{\begin{align} & \normalsize \text{In how many ways can u distribute 7 identical gifts among 5 children.}\hspace{.33em}\\~\\ & \normalsize \text{such that each child gets at least 1 gift.}\hspace{.33em}\\~\\ \end{align}}\)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0reserve 5 gifts, distribute the remaining 2, and then count the ways you can assign one of the reserved 5 to each child

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.3you may use the same trick, consider 7 stars : \[*~*~*~*~*~*~*\]

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.3you want to partition that into 5 nonempty parts, at what positions are you allowed to place the 4 bars ?

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.3is below a valid arrangement ? \[*~*~*~*~*~*~*\]

mathmath333
 one year ago
Best ResponseYou've already chosen the best response.1except the rear and front ends ?

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.3im asking specifically if above arrangement is valid

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.3how about below one : \[*~*~*~*~*~*~*\] what does it represent and is it a valid one ?

mathmath333
 one year ago
Best ResponseYou've already chosen the best response.10 gifts to first child 2 gift to second child 3 gift to third child 1 gifts to fourth child 1 gift to fifth child invalid

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.3right, that means you don't like the first child what about below one : \[*~*~~*~*~*~*~*\]

mathmath333
 one year ago
Best ResponseYou've already chosen the best response.12 gifts to first child 0 gift to second child 3 gift to third child 1 gifts to fourth child 1 gift to fifth child invalid

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.3so you cannot place bars next to each other and you cannot place bars on the ends

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.3the only valid places for bars are : \[*~*~*****\] those 6 dashes

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.3four bars to place six positions to choose from how many total ways can u do it ?

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.3a bit more generally, the number of positive integer solutions to the equation \(\large a+b+c+d+e=n\) is given by \(\large \dbinom{n1}{4}\)

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.3similarly, the number of "non negative" integer solutions to the equation \(\large a+b+c+d+e=n\) is given by \(\large \dbinom{n+4}{4}\)
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