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Combination of r Things from n Things When All Are Not Different

The number of...

Question

The number of three digit numbers of the form xyz where x > y > z is

120

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720

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600

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100

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Solution

The correct option is A 120
Any selection of three digits from the ten digits 0, 1, 2, 3, ……. 9 gives one number.
It is of $^{10} C_{3}$ ways

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Similar questions

x y z

x > y > z

^{10} C_{3}

z \leq y

^{9} C_{2}

\begin{matrix} x, y, z a l l d i f f . & \Rightarrow & ^{9} C_{3} \times 2! x = z < y & \Rightarrow & ^{9} C_{2} x < y = z & \Rightarrow & ^{9} C_{2} N o^{'} s \end{matrix}

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

3

x y z

x, z < y

x \neq 0

x y z

0, 1, 2, \dots 9

x \leq y \leq z

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