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Q: How many 5 digit numbers containing two times the digit 6 can be formed from the digits 123456?

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6*6*3 = 108 numbers.

6*5*4*3*2*1=720 possible numbers

192 ways

Numbers formed should be of at least 3 digits means they may be of 3 digits, 4 digits, 5 digits or 6 digits. There are 6 choices for digit in the units place. There are 5 and 4 choices for digits in ten and hundred’s place respectively. So, total number of ways by which 3 digits numbers can be formed = 6.5.4 = 120 Similarly, the total no.of ways by which 4 digits numbers can be formed = 6.5.4.3 = 360. the total no. of ways by which 5 digits numbers can be formed = 6.5.4.3.2 = 720. The total no.of ways by which 4 digits numbers can be formed = 6.5.4.3.2.1 = 720. So, total no.of ways by which the numbers of at least 3 digits can be formed = 120 + 360 + 720 + 720 = 1920.

192, including ones containing repeat digits.

99999

5040 different 4 digit numbers can be formed with the digits 123456789. This is assuming that no digits are repeated with each combination.

Assuming no repeated digits, lowest first, 20; in any order 120; Allowing repeated digits: 216

There are 5*4*3 = 60 such numbers.

There are 5 numbers of 1 digit, 25 numbers of 2 digits, and 75 numbers of 3 digits. This makes 105 numbers in all.

24

500

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