3 votes 3 votes 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? Combinatory goclasses2024-dm-4-weekly-quiz numerical-answers goclasses combinatory counting 1-mark + – GO Classes asked May 3, 2022 • edited May 16, 2023 by Lakshman Bhaiya GO Classes 277 views answer comment Share Follow See all 0 reply Please log in or register to add a comment.
3 votes 3 votes 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, $6 \ast 16 = 96.$ GO Classes answered May 3, 2022 GO Classes comment Share Follow See all 0 reply Please log in or register to add a comment.