CAT 2021 Slot 1 QA Question 1: The number of groups of three or more distinct numbers that can be chosen from 1, 2, 3, 4, 5, 6, 7 and 8 so that the groups always include 3 and 5, while 7 and 8 are never included together is

Question

The number of groups of three or more distinct numbers that can be chosen from 1, 2, 3, 4, 5, 6, 7 and 8 so that the groups always include 3 and 5, while 7 and 8 are never included together is

Accepted Answer

Since 3 and 5 must always be included, we only need to choose the remaining numbers from {1, 2, 4, 6, 7, 8}.
The group should have at least three numbers. So, at least one of these six remaining numbers must be chosen.
$2^6 - 1 = 63$
Now subtract the invalid cases where both 7 and 8 are chosen. In t