Question

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

• A. $5040$
• B. $7180$
• C. $8150$
• D. None of these

Answer 1

The correct option is B

$7180$

Explanation for the correct option:

Find the required number of factors:

Number of two factor products between $1$ to $200$ $={}^{200}C_2$

Numbers that are not multiples of $5$ between $1$ to $200$ $=160$ $\left[5,10,15,20,25.....200\mathrm{are}\mathrm{removed}\right]$

Total number of factor products which are not multiples of $5={}^{160}C_2$

$\therefore$required number of factors $={}^{200}C_2–{}^{160}C_2$

$=\mathbf{7180}$

Hence,option ‘B’ is correct.