Correct option (C) 35
To each selection of 4 persons we associate binary sequence of the form 1001001010 where 1(0) at ith place means the ith person is selected (not selected).
There exists one-to-one correspondence between the set of selections of 4 persons and set of binary sequence containing 6 zeros and 4 ones.
We are interested in the binary sequences in which no 2 ones are consecutive. We first arrange 6 zeros:
0 0 0 0 0 0
This can be done in just one way.
Now, 4 ones can be arranged at any of the 4 places marked with a cross in the following arrangement:
x 0 x 0 x 0 x 0 x 0 x 0
We can arrange 4 ones at 7 places in 7C4 = 35 ways.