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The number of all four digits numbers with distinct digits is

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The number of all four digits numbers with distinct digits is

9 \times 10 \times 10 \times 10

^{10} P_{4}

9 \times^{9} P_{3}

none of these

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Text solutionVerified

The number of all four digits number with a distinct digit is

There are ten digits 0 to 9

These ten digit have to be put in it places. Thousands, hundreds, tens units

Obviously, 0 cannot take the thousands place because it will become three digit number, so for thousands 9 ways can bedone

Now . and other 8 digit left, so at hundrend place 9 ways to set a digit.

We are now left with 8 digit fill the tens place which can be done in 5 ways

The remaining 7 digit in the unit place in 7 ways

so the answer is

9 \times 9 \times 8 \times 7 = 4536

9 \times_{9} P_{3}

A \to 9

B \to 9

C \to 8

D \to 7

= 9 \times 9 \times 8 \times 7

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Question Text	The number of all four digits numbers with distinct digits is
Answer Type	Text solution:1
Upvotes	150