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List all possible arrangements of the four letters m,a,r,and y. Let $\; C_1 \;$be the collection of the arrangements in which y is in the last position. Let $\; C_2\;$ be the collection of the arrangements in which m is the first position. Find the union and the intersection of $\; C_1\;$ and $\;C_2\;$.

Asaf Karagila
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Jonarie Ramos Vergara
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    The intersection looks like all words M _ _ Y. The union looks like all words of the forms _ _ _ Y and M _ _ _ – David P Sep 29 '14 at 16:56
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    You are asked to make a list. So make a list, say alphabetically. There will be $24$ arrangements, not too bad. Mark the ones that end in $y$ with a 1, and the ones that begin with m with a 2. Then you should not find it hard to list all of $C_1\cup C_2$, and (much easier) all of $X_1\cap C_2$. – André Nicolas Sep 29 '14 at 16:59

1 Answers1

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$C_1$={MARY,RAMY,ARMY,AMRY,MRAY,RMAY,}

So, n($C_1$)=3!=6

$C_2$={MARY,MRAY,MAYR,MYAR,MRYA,MYRA}

So, n($C_2$)=3!=6

$C_1∩C_2$={MARY,MRAY} ; n($C_1∩C_2$)=2

$C_1UC_2$={MARY,RAMY,ARMY,AMRY,MRAY,RMAY,MAYR,MYAR,MRYA,MYRA} ; n($C_1UC_2$)=10.

Hope it helps.

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