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

$5040$

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$7180$

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$8150$

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$N o n e o f t h e s e$

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Solution

The correct option is B
$7180$

Explanation for the correct option:
Given , The number from $1$ to $200$
The total number of two factor products = $^{200} C_{2}$
The numbers from $1$ to $200$ which are not multiples of $5$ is $160$ $[remove 5, 10, 15, 20 . . . . . 200]$
Therefore the total number of two factor products which are not multiples of $5$ is $^{160} C_{2}$ .
Hence, the required number of factors which are multiples of $5$ = $^{200} C_{2} -^{160} C_{2}$
= $7180$
Hence option(B) is correct.

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

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