Problem is here
I was wondering if he has to always have some color for a marble?
My logic is as follows :
If he wants to pick K different marbles then if I find all the different ways you can pick k different things out of n items and then for each of these configurations there are (n-k) remaining marbles each of them can be any color and since we already have the needed k different ones so it is basically allowing us to have repetitions with the colors of the remaining marbles so I must calculate how many combinations I can make out of the remaining ones with repetitions and say that b = ways to pick (k things out of n items) and c = (the ways i can combine the remaining marbles) then answer must be b * c;
Where is my logic wrong?
P.S I’ve been strugling with this problem for a few days now but please don’t tell me the answer,just show me that I’m on the wrong direction.
Yeah …You are thinking in the right direction…how many ways will be there to pick one item of each color ?
then u need to select remaining (n-k) items…and yes there will be repetitions obviously…
OK, so in the second example of the problem there are 7 items that I must pick with different color this means that there are 2035800 ways to select those 7 items.For each of those 2035800 there are (7^23) ways to choose the rest of the items(assuming that we are selecting all of the n items every time) i to arrive at a valid answer.This is what I deduce following this logic. Which means that there are 2035800 * (7^23) which is way beyond what the example has given us. There’s a mistake in my logic clearly.
See…ur approach is correct…but you are doing the wrong computation…the problem is a “in how many ways can u select” not a " in how many ways can u arrange" …Can u explain me how u reached to the figure “2035800”?
2035800 = (30 choose 7). But now looking at the comments I begin to understand what the note on the problem means : “Assume that marbles of equal color can’t be distinguished, and the order of the marbles is irrelevant” . It means that each of those ways to select the first 7 items are basically removed so there’s just one way to select the first 7 items. That means that the 2035800 factor is removed from the equation and becomes 1. So I’m left with 1 * 7^23
Yeah !!.u got it…but still u need to work on the other factor©…There is only one way to select the first 7 items…as they are non distinguishable…right…but the remaining 23 items…the problem is a classic multiset permutation problem…u have k color groups…x1+x2+x3…xk=(n-k)…where x1,x2,x3 …xk…are the number of items belonging to respective colors…u have to distribute the remaining (n-k) items in the k groups such that x1,x2…xk>=0, …
the 7^23 term that u are calculating is a sequence which has the importance of order…
permutation=importance of order+ non repetition…
sequence=importance of order+ repetition…
combination=no importance of order + non repetition…
multiset= no importance of order + repetition…
I hope that will help u !!
P.S :I Hope i didnt Tell u the answer directly 
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thx i just saw ur new answer thanks a lot!