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DecentNabeel
 one year ago
Timothy is rearranging his marble collection.he has five identical blue marbles,five identical green marbles and three identical black marbles he can fit exactly five marbles into a case and must have at least one of each.How many different ways can he arrange the case in?
DecentNabeel
 one year ago
Timothy is rearranging his marble collection.he has five identical blue marbles,five identical green marbles and three identical black marbles he can fit exactly five marbles into a case and must have at least one of each.How many different ways can he arrange the case in?

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DecentNabeel
 one year ago
Best ResponseYou've already chosen the best response.2@mathmate @mathmate

DecentNabeel
 one year ago
Best ResponseYou've already chosen the best response.2any one you can help me

DecentNabeel
 one year ago
Best ResponseYou've already chosen the best response.2@welshfella can you slove it

welshfella
 one year ago
Best ResponseYou've already chosen the best response.0its been a long time. I could do it by listing all the combinations I suppose but there must be a quicker way.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0thanks for posting the question. As @welshfella says it gives us a chance to test our knowledge

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0I am going to summarize the problem as follows: 5 identical blue marbles 5 identical green marbles 3 identical black marbles he can fit 5 identical marbles into a case and must have at least one of each How many different ways can he arrange the case in

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0There are a total of 18! (18 factorial possible permutations) here, but we shall work our way down!

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0The best way to think of this is to create 5 boxes! one for each marble

mathmate
 one year ago
Best ResponseYou've already chosen the best response.0@BPDlkeme234 sorry to interrupt, there is a total of (5+5+3)=13 marbles only! :)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0thatnkyou @mathlete, I had to make corrections anyway

UsukiDoll
 one year ago
Best ResponseYou've already chosen the best response.1so.... 13 factorial?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0If the first box has to contain a blue marble then you have a choice of 5 marbles dw:1439457071976:dw

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0If the second box contains a green marble , you also have a choice of 5 marblesdw:1439457195269:dw

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Now, since the third box must contain a black marble you have a choice of 3 marblesdw:1439457353162:dw

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0This leaves two choices and you can select any color for the last two choices. I will explain how many possibilities left

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0you have selected 3 marbles already leaving a total of , thanks to @mathlete informing me, 10 marbles. So you then have 10 possible choices you can make!dw:1439457604678:dw

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Finally, having selected the 4th marble, you have 9 possible choices (134) dw:1439457719650:dw

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0This means the total number of ways he can arrange the case is: 5 x 5 x 3 x 10 x 9

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0So how did do @mathlete?

DecentNabeel
 one year ago
Best ResponseYou've already chosen the best response.2i think you are correct @BPDlkeme234 but not confirmed... Please verify another expert but thanks for help

DecentNabeel
 one year ago
Best ResponseYou've already chosen the best response.2@pooja195 can you help me

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0you could ask @satellite73 he is a moderator here

DecentNabeel
 one year ago
Best ResponseYou've already chosen the best response.2@satellite73 can you help me

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0i suck at these, but looks like the above answer is correct

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0\[5\times 5\times 3\times 10\times 9\] right?

DecentNabeel
 one year ago
Best ResponseYou've already chosen the best response.26750 that is the answer you are sure

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0yeah that looks pretty good to me

mathmate
 one year ago
Best ResponseYou've already chosen the best response.0@decentnabeel Since you seem to be still at it, here's my take: We need to place 5 marbles in the case, with at least one colour of each, there can only be a maximum of 3 marbles of a single colour. Thus with 5 blue, 5 green and 3 black, we have enough for any combination, and we need not worry about the 13 marbles any more. Let B=blue, G=green, K=black. Looking at the shelf, the colour combinations are either case 1: (3,1,1) of each colour, or There are three ways to get these colour combinations, i.e. (3B,G,K), (3G,B,K) and (3K,B,G). For each colour combination, the number of arrangements (permutations) is 5!/(3!1!1!) for a total of 3(5!/(3!1!1!)) arrangements case 2: (2,2,1) of each colour. There are three ways to get these colour combinations, i.e. (2B,2G,K), (2G,2K,B), (2K,2B,G). For each colour combination, the number of arrangements (permutations) is 5!/(2!2!1!) for a total of 3(5!/(2!2!1!)) arrangements So the total number of arrangements is the sum of cases 1 & 2, namely 3(5!/(3!1!1!))+3(5!/(2!2!1!))
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