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The numbers 1, 2, 3,..., 100 can be used to form any two-factor product. Out of the total obtained, how many factors are multiples of six?

 

Option: 1

1422


Option: 2

1244


Option: 3

1532

 


Option: 4

1643 


Answers (1)

best_answer

The total number of 2-factor products is given by,

\begin{aligned} &{ }^{100} C_2=\frac{100 !}{2 !(100-2) !}\\\\ &{ }^{100} C_2=4950 \end{aligned}

The numbers from 1 to 100 which are not multiples of 6 is 84.

Thus, the total number of 2-factor products which are not multiples of 6 is given by,

\begin{aligned} &{ }^{84} C_2=\frac{84 !}{2 !(84-2) !}\\\\ &{ }^{84} C_2=3528 \end{aligned}

Thus, the required number of ways is,


\begin{aligned} &{ }^{100} C_2-{ }^{84} C_2=4950-3528\\\\ &{ }^{100} C_2-{ }^{84} C_2=1422 \end{aligned}

Therefore, the total number of ways the factors can be formed in 1422 ways.

Posted by

SANGALDEEP SINGH

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