Mathematics - Permutation & Combination Question with Solution | TestHub

MathematicsPermutation & CombinationFundamental PrincipleMedium2 minQB

MathematicsMediumsingle choice

The number of three digit numbers of the form $x yz$ such that $x < y$ and $z \leq y$ is

Answer:

Solution:

If zero is included, it will be at $^{9} C_{2 n o . s}$ . If zero is excluded:

$⎩ ⎨ ⎧ x, y, z a ll d i ff . x = z < y x < y = z \Rightarrow^{9} C_{3} \times 2! \Rightarrow^{9} C_{2} \Rightarrow^{9} C_{2} N o^{'} s$

Total number of ways $= 276$ . Alternatively, $y$ can be from 2 to 9, so the total number of ways is:

$r = 2 \sum 9 (r^{2} - 1) = 276$

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

⏱ 2mℹ️ Source: QB

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