Question

In a locality, there are ten houses in a row. on a particular night a thief planned to steal from three houses of the locality. in how many ways can heplan such that no two of them are next to eachother

Answer 1

56 ways
number the houses from 1to 10 thenwrite all probalitites
135
136
137
138
139
1310
146
147
148
149
1410
157
159
1510
168
169
1610
179
1710
1810
246
247
248
249
2410
257
258
259
2510
268
269
2610
279
2710
2810
357
358
359
3510
368
369
3610
379
3710
3810
468
469
4610
479
4710
4810
579
5710
5810
6810