Question

Varun has $10$cards with numbers $1$to $10$. In how many ways can a total of $15$be made using only three cards at a time?

Answer 1

A total of $15$should be made using only three cards at a time, which means no repetition is allowed.
$$\begin{gathered} (1,4,10)=3! \\ (2,4,9)=3! \\ (2,5,8)=3! \\ (2,6,7)=3! \\ (3,2,10)=3! \\ (3,4,8)=3! \\ (3,5,7)=3! \\ (4,5,6)=3! \end{gathered}$$
Thus, the total number of possible group of cards $=8\times 3!=8\times 6=48$