CAT 2024 - Slot 1 Quant Question 1
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CAT 2024 Slot 1 - Quant
Set A = {2, 3, 5, 7, 11, 13} so |A|= 6
Set B = {1, 8, 27} so |B|= 3
Without any restrictions, each element in A can map to any of the 3 elements in B. Thus, the total number of functions is: 36 = 729
Excluding Functions That Miss One Element in B: If a function does not map to an element in B, there are 2 elements in B left for mapping. The total number of such functions (for each specific element not mapped) is: 26 = 64
Since there are 3 elements in B, the total number of such functions is: 3 × 64 = 192
Adding Back Functions That Miss Two Elements in B: If a function misses two elements in B, there is only 1 element left for mapping. The total number of such functions is: 16 = 1
Since there are 3C2 ways to choose which two elements are missed, the total number of such functions is: 3
Using the inclusion-exclusion principle, the number of functions where all elements of B are mapped by at least one element of A is:
729 – 192 + 3 = 540