Let us consider the first the group of 7,

If DAvid and Alice are in this group then we need to choose only 5 out of 7 from total of 8 people(as David and Alice are considered in the group)

so we have 8C5 = 56 ways.

Now if David and Alice are in the group of 3 people then selecting the group from the total of 8 people will be = 8C1 = 8

So the total no. of ways = 56 + 8 = 64 ways
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I didn't get the reason for 3*2 and the last *2.