Question

Eight cards bearing numbers 1,2,3,4,5,6,7,8 are well shuffled. Then in how many cases the top 2 cards will from a pair of twin prime equals

• A. $720$
• B. $1440$
• C. $2880$
• D. $2160$

Answer 1

The correct option is C $2880$

According to teh question,

twin prime pairs are $(3,5),(5,3),(5,7)$ and $(7,5)$ as prime pairs can be written in any order.

$\therefore$Total number of cases$=6!\times 4=6\times 5\times 4\times 3\times 2\times 4=2880$