He number of natural numbers less than 1000, in which no two digits are repeated is
Answers
Answer:
The number of natural numbers less than 1000, in which no two digits are repeated is:
738
Step-by-step explanation:
As there are a total of 999 natural numbers from 1 to 999.
Also, the number of natural numbers in which two digits are repeated is: 261
( since, such numbers are:
11,22,33,44,55,66,77,88,99---- which are 9 numbers
100,101,110,111,112,113,114,115,116,117,118,119,121,122,131,133,141,144,151,155,161,166,171,177,181,188,191,199---- which are 28 numbers.
200,202,211,212,220,221,222,223,224,225,226,227,228,229,232,233,242,244,252,255,262,266,272,277,282,288,292,299---- which are 28 numbers.
similarly we can write a set of 28 numbers between 300-399,400-499,500-599,....900-999
Hence, the total number of such numbers are: 9+28×9=261 )
Hence, the number of natural numbers less than 1000, in which no two digits are repeated is:
999-261=738
Answer:
738
Step-by-step explanation:
Numbers less than 1000 are one digit no., two digits numbers and three digits number.
No. of one digit number =9
No. of two digit number in which =9×9=81
no. two are repeated
(For one's place we have 9 choice for ten's place we have 9 choices (0 excluded) )
No. of three digit number in which No. two digit are repeated =9×9×8
=648
(For hundred place we have 9 choice (0 excluded) for ten's place we have 9 choices & or One's place we have 8 choices )
∴ Total number less than 1000 in which no. two digits are repeated are : =9+81+648
=738