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GO Classes Test Series 2024 | Discrete Mathematics | Test 4 | Question: 10
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Consider the set $\text{X} = \{2, 3, 4, 5, 6, 7, 8, 9\},$ which contains $8$ elements. How many subsets of $\text{X}$ have exactly two prime numbers?
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The numbers $2, 3, 5$ and $7$ are the only prime numbers in $\text{X}.$
Subsets which have exactly two prime numbers : We have $^{4}\text{C}_{2} = 6$ choices for those three prime numbers, and for the remaining non-prime numbers, we have $2$ choices for each. So, $6 \ast 16 = 96.$
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