Mathematics - Permutation & Combination Question with Solution | TestHub

MathematicsPermutation & CombinationFundamental PrincipleMedium2 minQB

MathematicsMediumsingle choice

Number of ordered pair (x, y) such that LCM of x, y is $2^{3} 3^{4} 5^{6}$ is

Answer:

Solution:

The equation is $x = 2^{a_{1}} 3^{b_{1}} 5^{c_{1}}$ .

The values for $y$ are:

$y = 2^{a_{2}} 3^{b_{2}} 5^{c_{3}}$

For $(a_{1}, a_{2})$ , there are 7 ways: $(0, 3), (1, 3), (2, 3), (3, 3), (3, 2), (3, 1), (3, 0)$ .

For $(b_{1}, b_{2})$ , there are 9 ways: $(0, 4), (1, 4), (2, 3), (3, 4), (4, 4), (4, 3), (4, 2), (4, 1), (4, 0)$ .

Stream:JEESubject:MathematicsTopic:Permutation & CombinationSubtopic:Fundamental Principle

⏱ 2mℹ️ Source: QB

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