Question

Two numbers(can be same) are chosen from $1,3,5,7,\dots ,147,149$ and $151$ and multiplied together in all possible ways. Find the number of ways which will give us the product a multiple of $5$.

Answer 1

Numbers which are multiple of $5$ are $5,15,25,...,145$

$a=5,d=10,n=?$ $a_n=145$

$\Rightarrow 145=5+(n-1)10$

$\Rightarrow n=15$

Thus one number we have to choose from these $15$ numbers

and another one from any number which are $\frac{151+1}{2}=76$

Thus total ways$=15\times 76=1140$.