Answer:
(a) Watch all three channels: To find the number of families that watch all three channels, we can use the principle of inclusion-exclusion. The total number of families watching at least one channel is given by:
\[ \text{Total} = \text{NTV} + \text{Kantipur} + \text{Avenues} - (\text{NTV and Kantipur}) - (\text{NTV and Avenues}) - (\text{Kantipur and Avenues}) + (\text{NTV and Kantipur and Avenues}) \]
Plugging in the values, we get:
\[ 300 = 150 + 145 + 140 - 35 - 30 - 90 + (\text{NTV and Kantipur and Avenues}) \]
\[ 300 = 360 - 150 + (\text{NTV and Kantipur and Avenues}) \]
\[ 300 = 210 + (\text{NTV and Kantipur and Avenues}) \]
\[ (\text{NTV and Kantipur and Avenues}) = 90 \]
So, 90 families watch all three channels.
(b) Watch Kantipur and Avenues only: To find the number of families that watch Kantipur and Avenues only, we can subtract the number of families that watch all three channels, NTV and Kantipur only, and NTV and Avenues only from the total number of families watching Kantipur:
\[ \text{Kantipur and Avenues only} = \text{Kantipur} - (\text{NTV and Kantipur}) - (\text{Kantipur and Avenues}) - (\text{NTV and Kantipur and Avenues}) \]
Plugging in the values, we get:
\[ \text{Kantipur and Avenues only} = 145 - 35 - 90 - 30 \]
\[ \text{Kantipur and Avenues only} = 145 - 155 \]
\[ \text{Kantipur and Avenues only} = -10 \]
Since the number of families cannot be negative, we assume there might be a mistake in the data provided or the question formulation.
(c) Watch at least one channel: We already calculated this in part (a) as the total number of families watching at least one channel, which is 300.