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64 if repetition is allowed, 6 otherwise.

64 if repetition is allowed, 6 otherwise.

64 if repetition is allowed, 6 otherwise.

64 if repetition is allowed, 6 otherwise.

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64 if repetition is allowed, 6 otherwise.

Q: How many different positive integers less than 2000 can be formed by using digits 123 and 4?

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There are 320 such numbers.

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.

Assuming all 45 digits are different (which they will not be if they are ordinary integers), then 456, if repetitions are allowed. That is 8303765625. If repetitions are not allowed then the number falls to 45*44*43*42*41*40 = 5864443200

192, including ones containing repeat digits.

The number of 4 digit codes, using different digits, is 10*9*8*7 = 5040. However, computer passwords can, usually, have repeated digits and, if that is allowed, you can have 104 = 10000 codes.

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There are 320 such numbers.

Negative integers, zero and the positive integers, together form the set of integers.

12 numbers.

1 x 10 x 10 x 10 x 9 = 9000 1 = it must be 2 10's = any digits 9 = any digit BUT zero

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.

There are 7,290 different 4-digit numbers that can be formed from the digits 1-9 without repetition.

Assuming all 45 digits are different (which they will not be if they are ordinary integers), then 456, if repetitions are allowed. That is 8303765625. If repetitions are not allowed then the number falls to 45*44*43*42*41*40 = 5864443200

If the digits are all different then 18. Otherwise, 192.

54

36

10,000

192, including ones containing repeat digits.