Question

How many three digit numbers can generated from 1,2,3,4,5,6,7,8,9 such that the digits are in ascending order. 1)80 2)81 3)83 4)84?

Answer 1

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Solution for the same is given below

Numbers starting with 12 – 7 numbers

Numbers starting with 13 – 6 numbers;

14 –5, 15 –4, 16 –3, 17 –2, 18 -1.

Thus total number of

numbers starting from 1 is given by the sum of 1 to 7 = 28.

Number of numbers starting from 2- would be given by the sum of 1 to 6 = 21

Number of numbers starting from 3- sum of 1 to 5 = 15

Number of numbers starting from 4 – sum of 1 to 4 = 10

Number of numbers starting from 5 – sum of 1 to 3 = 6

Number of numbers starting from 6 = 1 + 2 = 3

Number of numbers starting from 7 = 1

Thus a total of: 28 + 21 + 15 + 10 + 6 + 3 + 1 = 84 such numbers.

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