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Finding Remainder of Numbers of the Form a^b

I : The numbe...

Question

I : The number of 3 digit numbers of the form xyz where x >y>z is 1.
II : The number of 3 digit numbers of the form xyz where x > y >z is $^{10} C_{3}$ . 3!
Which of the above statement is correct?

only I

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only II

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Both I and II

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Neither I nor II

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Solution

The correct option is B Neither I nor II
I : Select 3 digits from 10 digits {0,1, 2, .......,9}
in $^{10} C_{3}$ ways and arrange as given in 1 way
$\Rightarrow^{10} C_{3}$ (false)
II : Number of ways $=^{10} C_{3}$ (false)
Hence both statements are incorrect.

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Similar questions

Q. The number of

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x y z

where

x, z < y

and

x \neq 0

Q. The number of three digit numbers of the form

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where

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Find the total number of ways in which a 3- digit number xyz can be formed from the digits $1, 4, 5, 6, 7, 8 a n d 9$ such x,y,z that are in A.P and $x \neq y \neq z .$

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x = y = z ?

(I)

x^{3} + y^{3} + z^{3} = 3 x y z

(II)

x^{3} + y^{2} z + y z^{2} = 3 x y z

(II)

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I : The number of 3 digit numbers of the form xyz where x >y>z is 1.II : The number of 3 digit numbers of the form xyz where x > y >z is 10C3 . 3!Which of the above statement is correct?

The correct option is B Neither I nor III : Select 3 digits from 10 digits {0,1, 2, .......,9}in 10C3 ways and arrange as given in 1 way⇒10C3 (false)II : Number of ways =10C3 (false)Hence both statements are incorrect.

I : The number of 3 digit numbers of the form xyz where x >y>z is 1.
II : The number of 3 digit numbers of the form xyz where x > y >z is $^{10} C_{3}$ . 3!
Which of the above statement is correct?

The correct option is B Neither I nor II
I : Select 3 digits from 10 digits {0,1, 2, .......,9}
in $^{10} C_{3}$ ways and arrange as given in 1 way
$\Rightarrow^{10} C_{3}$ (false)
II : Number of ways $=^{10} C_{3}$ (false)
Hence both statements are incorrect.