CAT 2021 Slot 1 · Quant · Question 12
CAT 2021 Slot 1 previous year question on Permutation and Combination, with the answer and a step-by-step solution.
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
Answer & solution
Answer: 47
Fix 3 and 5 in every group, then choose a non-empty subset of \{1,2,4,6,7,8\} to reach a size of three or more: {2}^{6}-1=63 ways. Of these, the subsets containing both 7 and 8 number {2}^{4}=16. So the answer is 63-16=47.
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