My Math Forum Combination and Permutation

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 April 10th, 2011, 08:24 AM #1 Senior Member   Joined: Mar 2011 Posts: 105 Thanks: 0 Combination and Permutation Combination MAth Problem? we have 5 red pens, 4 green pens,and 2 blue pens How many different ways can we choose 2 of these pens to buy if a, the order is important b, the order is not important
April 10th, 2011, 01:46 PM   #2
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Re: Combination and Permutation

Hello, daivinhtran!

Quote:
 We have 5 red pens, 4 green pens,and 2 blue pens. [color=blue]I assume that the pens are identical except for color.[/color] How many different ways can we choose 2 of these pens to buy if: [color=beige]. . [/color](a) the order is important.

$\text{Since the order of the colors }is\text{ important,}$
[color=beige]. . [/color]$\text{there are }nine\text{ cases to consider.}$

[color=beige]. . [/color]$\begin{array}{ccccc}\text{RR:}=&{5\choose2}=&10 \\ \\ \\ \text{GG:}=&{4\choose2}=&6 \\ \\ \\ \text{BB:}=&{2\choose2}=&1 \\ \\ \\ \hline \\ \\=&17 \end{array} \;\;\;\text{Group 1: one color}=$

[color=beige]. . [/color]$\begin{array}{ccccc}\text{RG:}=&5\,\cdot\,4=&20 \\ \\ \\ \\ \text{GB:}=&4\,\cdot\,2=&8 \\ \\ \\ \\ \text{RB:}=&5\,\cdot\,2=&10 \\ \\ \hline \\ \\=&38 \end{array}\;\;\;\text{Group 2: two colors}=$

[color=beige]. . [/color]$\begin{array}{ccccc}\text{GR:}=&4\,\cdot\,5=&20 \\ \\ \\ \\ \text{BG:}=&2\,\cdot\,4=&8 \\ \\ \\ \\ \text{BR:}=&2\,\cdot\,5=&10 \\ \\ \hline \\ \\=&38 \end{array}\;\;\;\begin{array}{c}\text{Group 3: two colors} \\ \text{different order} \end{array}=$

$\text{There are: }\:17\,+\,38\,+\,38 \:=\:93\text{ ways.}$

Quote:
 ( b) the order is not important.

$\text{Since order is }not\text{ important, we consider Group 1 and Group 2 only.}$

$\text{There are: }\:16\,+\,38 \:=\:55\text{ ways.}$

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