A committee of four persons is to be selected from 8 computer engineers and 3 mechanical engineers so as to include at least one mechanical engineers. The possible no. of ways are?

The total number of ways of selecting 4 persons from 11 engineers is 11C4 = 330

The total number of ways of selecting 4 persons from 8 computer engineers (and no mechanical engineers) is 8C4 = 70

The total number of ways of selecting 3 persons from 8 computer engineers (and exactly one mechanical engineer from 4) is 8C3 * 3  = 168

So, the required number is 330 - 70 - 168 = 92

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The correct answer is 260.

Here's how:

Total number of persons selected 11C4=330

Number of ways of selecting ONLY computer engineers and NO mechanical engineer is 8C4 = 70

Now, the condition CLEARLY says AT LEAST ONE mechanical engineer. So we just need to subtract ONLY computer engineers from Total engineers. 

Therefore, 330-70=260