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What is the proper adjective to use with the word chance? Can chance be low, small, slim? What would be your suggestion?

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All three are commonly used, as a bit of Googling will show you. –  onomatomaniak May 19 '13 at 11:04
    
You might also try fat chance. It means almost the same thing as slim chance & is the same as saying no chance or Impossible!. –  user21497 May 19 '13 at 13:40

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up vote 3 down vote accepted

All three are grammatical and idiomatic. A chance can be all of these things, and more. The top 50 collocations from the Corpus of Contemporary American English (COCA) and the British National Corpus (BNC) look as follows:

    COCA                                BNC

 1  a good chance              1403     a good chance             274   
 2  a better chance            1059     a better chance           173
 3  a fair chance               218     a fair chance              56
 4  a real chance               189     a great chance             47
 5  a greater chance            133     a real chance              32
 6  a great chance              127     a reasonable chance        31
 7  a reasonable chance         103     a greater chance           27
 8  a decent chance              72     a realistic chance         24
 9  a rare chance                61     a new chance               18
10  a slim chance                59     a rare chance              14
11  a big chance                 56     a slim chance              13
12  a small chance               53     a glorious chance          12
13  a realistic chance           46     a sporting chance          11
14  a strong chance              46     a small chance             10
15  a new chance                 43     a strong chance            10
16  a slight chance              36     a high chance               9
17  a final chance               29     a further chance            9
18  a serious chance             26     a unique chance             9
19  a legitimate chance          25     a big chance                7
20  a higher chance              25     a lucky chance              7
21  a remote chance              23     a remote chance             6
22  a once-in-a-lifetime chance  19     a marvellous chance         6
23  a significant chance         18     a fine chance               5
24  a sporting chance            18     a final chance              5
25  a unique chance              18     a wonderful chance          5
26  a fresh chance               13     a proper chance             4
27  a high chance                13     a higher chance             4
28  a golden chance              11     a happy chance              4
29  a solid chance               11     a simple chance             4
30  a better-than-average chance 10     a slight chance             4
31  a better-than-even chance     9     a reduced chance            3
32  a fine chance                 8     a golden chance             3
33  a huge chance                 8     a decent chance             3
34  a single chance               8     a fat chance                3
35  a little chance               7     a fresh chance              3
36  a low chance                  7     a useful chance             3
37  a perfect chance              7     a winning chance            3
38  a wonderful chance            7     a brief chance              2
39  a genuine chance              6     a close-range chance        2
40  a poor chance                 6     a full chance               2
41  a terrific chance             6     a fucking chance            2
42  a tiny chance                 6     a genuine chance            2
43  a large chance                5     a little chance             2
44  a full chance                 5     a low chance                2
45  a fat chance                  5     a missed chance             2
46  a bigger chance               5     a once-in-a-lifetime chance 2
47  a major chance                5     a poor chance               2
48  a missed chance               5     a mathematical chance       2
49  a nice chance                 5     a slender chance            2
50  a brief chance                4     a straightforward chance    2

These usage stats suggest that overall, slim is somewhat preferred over small, and both are clearly preferred over low, on both sides of the pond. Further candidates range from poor to little to remote to slender to once-in-a-lifetime, but see for yourself. I will leave it as an exercise to the reader to figure out which of these does or does not fit their particular context, especially as no particular context is supplied in this question.

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If you use little chance, note that it doesn't take the indefinite article like most of these constructions do. –  Bradd Szonye May 19 '13 at 20:38

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