Remove rows by multiple logical conditions (rstudio)

Let's say this is my dataframe:

df <- data.frame(replicate(10,sample(0:50,20,rep=TRUE)))

S  X1 X2 X3 X4 X5 X6 X7 X8 X9 X10
1   3 26 39 25 24  4 46 42  8  42
2  40  6 50 50 22  2 40 24 26  17
3  32 45 18  7 19  6 33 12  0  13
4   3 45 43 32 16 33 25 18 35  45
5   7 36  2 25 16 20 24 14 27  29
6  45  4 12 13 50 35 38  1 27  34
7  18 43 38 16 34 18 19 45  4  34
8  18  9 33 38 18 13 23 44 41   4
9  28 34  6  3 14 11 47  4 21  50
10  6 48 42 46 48 42 12 33  1  32
11 28 20 37  2 26 33  5  2 22  27
12 40 30 41 45 28  6  5 46 21  46
13  1 47 46 37  0  3 11 45 12  11
14 20  0  9 38 42 15 44  1  2  45
15 49 29 25 41 38 26 20 34 50   0
16  2  5 47  6 36 34 28 36 32  38
17 15 22 50 13 26  9 37 40 41  23
18 44 27 47 37 26 34 31 36 44  12
19 47 41 19  2 50 44 48 36 34  38
20 25 31 28 34  8 19  3 13 14  23

I need to exclude subjects ('S') with values higher than 30 in 8 or more columns(X1:X10). That is, only exclude those who has 8 times or more values above 30 (e.g. Subject 19). I was thinking that maybe 'ifelse' function can be useful, but I really don't know how to implement it.

Any help is highly appreciated! Thanks a lot!