Jose is paying for a $10 meal using bills in his wallet. He has five $1 bills and four $5 bills. If he selects two bills at random, one at a time from his wallet, without replacement, what is the probability that he will choose two $5 bills to pay for the meal? Show your work.
\begin{array}l\color{#FF0000}{\text{RAINBOWRAINBOWRAINBOWRAINBOW}}\end{array}\begin{array}l\color{#FF7F00}{\text{RAINBOWRAINBOWRAINBOWRAINBOW}}\end{array}\begin{array}l\color{#FFFF00}{\text{RAINBOWRAINBOWRAINBOWRAINBOW}}\end{array}\begin{array}l\color{#00FF00}{\text{RAINBOWRAINBOWRAINBOWRAINBOW}}\end{array}\begin{array}l\color{#0000FF}{\text{RAINBOWRAINBOWRAINBOWRAINBOW}}\end{array}\begin{array}l\color{#6600FF}{\text{RAINBOWRAINBOWRAINBOWRAINBOW}}\end{array}\begin{array}l\color{#8B00FF}{\text{RAINBOWRAINBOWRAINBOWRAINBOW}}\end{array}
wow
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wow
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