All possible two factor products are formed from the numbers 1,2,.....100. The number of factors out of the total obtained which are multiple of 3 is.

2211

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4950

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2739

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1540

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Solution

The correct option is C 2739
According to the problem,
Total two factor products multiplies of $3 =$ (total two factor products) – (two factor products of non-multiplies of 3)
Since,
Total factor products $=^{100} C_{2}$
Total two factors of non-multiplies of 3 $=^{67} C_{2}$
Implies that,
$=^{100} C_{2} -^{67} C_{2}$
$= 2739$
Hence, total two factor products multiplies of $3$ is $2739$

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