Question

All possible two factor products are formed from the numbers $1,2,3,4,......200$. The number of factors out of total obtained which are multiples of $5$ is

• A. 5040
• B. 7180
• C. 8150
• D. 7200

Answer 1

The correct option is B 7180

The total number of two factor products ${}^{200}{C}_2.$

The number of numbers form $1$ to $200$ which are not multiples of $5$ is $160.$
Therefore, the total number of two factor products which are not multiple of $5$ is ${}^{160}{C}_{2.}$
Hence, the required number of factor
${=}^{200}{C_2-}^{100}{C}_2=7180$