Question

How many natural numbers are there between 1 to 1000 which have none of their digits repeated?

Answer 1

Answer:

738

Step-by-step explanation:

FROM 1 TO 1000 NONE OF THEIR DIGITS REPEAT

FIRST FROM 1 TO 9 NONE OF THEIR DIGITS REPEAT->SO 9 NUMBERS 1-9(NO 0 BECAUSE NATURAL NUMBERS)

                                             =>9 NUMBERS POSSIBLE_1.

SECOND FROM 10 TO 99-> FIRST PLACE 9 NUMBERS POSSIBLE(1-9)

                                               SECOND PLACE ALSO 9 NUMBERS POSSIBLE (0-9 AND NO REPETITION SO ONE NUMBER WILL BE EXCLUDED FROM 1-9)

                                              =>9*9=81 NUMBERS POSSIBLE_2.

THIRD FROM 100 TO 999-> FIRST PLACE 9 NUMBERS POSSIBLE(1-9)

                                               SECOND PLACE ALSO 9 NUMBERS POSSIBLE (0-9 AND NO REPETITION SO ONE NUMBER WILL BE EXCLUDED FROM 1-9)

                                               THIRD PLACE ONLY 8 NUMBERS POSSIBLE

(0-9 AND NO REPETITION SO TWO NUMBERS WILL BE EXCLUDED FROM 1-9)

                                              =>9*9*8=648 NUMBERS POSSIBLE_3.

THEREFORE ADDING 1.,2. AND 3.,WE GET

9+81+648=648+90=738 numbers are there between 1 to 1000 which have none of their digits repeated