The total number of slips in the bag is 4+7+5+2 = 18.
There are 18·17/2 = 153 ways to draw 2 slips of paper from those 18.
There are 4·3/2 = 6 ways to draw 2 blue slips of paper.
The probability of winning by randomly drawing 2 slips of paper is ...
... 6/153 = 2/51
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There are 18 (or 4) ways to draw the first slip, and 17 (or 3) ways to draw the second one. The same two slips can be drawn in either order, so the number of ways of drawing them just computed must be divided by 2. The result is the count of ways that two slips of paper can be drawn from the pool of all (or blue) slips of paper.
