SOLUTION: the total number of ways in which six 't' and four '-' signs can be arranged in a line such that no two '-' signs occur together is?

Think of it this way:

↏t↏t↏t↏t↏t↏t↏

We must pick 4 of the 7 boxes to put a single "-" in.

Answer: the number of combinations of 7 things taken 4 at a time 

or 7C4 or C(7,4) =  = 35

Here are all 35 ways:

 1.  -t-t-t-ttt
 2.  -t-t-tt-tt
 3.  -t-t-ttt-t
 4.  -t-t-tttt-
 5.  -t-tt-t-tt
 6.  -t-tt-tt-t
 7.  -t-tt-ttt-
 8.  -t-ttt-t-t
 9.  -t-ttt-tt-
10.  -t-tttt-t-
11.  -tt-t-t-tt
12.  -tt-t-tt-t
13.  -tt-t-ttt-
14.  -tt-tt-t-t
15.  -tt-tt-tt-
16.  -tt-ttt-t-
17.  -ttt-t-t-t
18.  -ttt-t-tt-
19.  -ttt-tt-t-
20.  -tttt-t-t-
21.  t-t-t-t-tt
22.  t-t-t-tt-t
23.  t-t-t-ttt-
24.  t-t-tt-t-t
25.  t-t-tt-tt-
26.  t-t-ttt-t-
27.  t-tt-t-t-t
28.  t-tt-t-tt-
29.  t-tt-tt-t-
30.  t-ttt-t-t-
31.  tt-t-t-t-t
32.  tt-t-t-tt-
33.  tt-t-tt-t-
34.  tt-tt-t-t-
35.  ttt-t-t-t-

Edwin