Determine the number of natural numbers smaller than 10^4 in the decimal notation of which all the digits sre distinct
Answers
Answer:
5922
Step-by-step explanation:
We need to find the number of natural numbers from 1 to 9999 of which all digits are distinct...
Consider single digit numbers, = 9
2 digit numbers = xy where x can take any digit from 1 to 9
= where as y can take any digit from 0 to 9 except digit of 'x',
hence there are 9 possibilities for x as well as y
=total 9*9=81
Similarly, 3 digit numbers = xyz, here x can take any digit from 1 to 9
= where as y can take any digit from 0 to 9 except digit of 'x',
hence there are 9 possibilities for x as well as y, z can take any digit from 0 to 9 except digits taken by 'x' and 'y'
= hence there are 8 possibilities
total 9*9*8=648
Similarly, 4 digit numbers = xyzw, here x can take any digit from 1 to 9
= where as y can take any digit from 0 to 9 except digit of 'x',
hence there are 9 possibilities for x as well as y, z can take any digit from 0 to 9 except digits taken by 'x' and 'y'
= hence there are 8 possibilities
w can take any digit from 0 to 9 except digits taken by 'x', 'y' and 'z'
= hence there are 7 possibilities
total 9*9*8*7=5184
So, total = 9+81+648+5184=5922.
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Step-by-step explanation:
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