From the digits 1, 2, 3, 4, 5, 7, 9, how many numbers of 3 digits can be formed if repetition is allowed in a number? | Socratic (2024)

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From the digits 1, 2, 3, 4, 5, 7, 9, how many numbers of 3 digits can be formed if repetition is allowed in a number? | Socratic? ›

Explanation: The first digit of the 3-digits can take 7 distinct values: 1, 2, 3, 4, 5, 7, 9. As repetition is allowed, the second digit can also take 7 distinct values, and the third can take 7 distinct values aswell, giving a total of 7⋅7⋅7=343 distinct combinations of numbers.

900 is the number of 3-digit numbers formed using the digits with repetition. There are 9 numbers, i.e. 111, 222, …, 999 that has 3 numbers being the same.

Therefore, there are 120 3 digit numbers that can be formed with these digits and no repetition. Alternatively, you can choose the first digit for the number with 6 ways (use any of the digits. For the second digit, you have 5 ways (since repetition is not allowed). For the third digit, you have 4 ways.

If you are meaning simply a 3 digit number using digits 0–9 then the answer is 10•10•10 = 1,000 with repetition. 10•9•8 = 720 without repetitions.

So the number of three digit numbers which can be formed = 6 x 5 x 4 = 120.

List of Three Digits Numbers. As we already discussed, the three digits numbers are from 100 (hundred) to 999 (nine hundred ninety-nine). Before we see the list of three digits numbers, first let us discuss how many three digits numbers we have from 100 to 999. Hence, there are 900 three-digit numbers in total.

There are 504 different 3-digit numbers which can be formed from numbers 1, 2, 3, 4, 5, 6, 7, 8, 9 if no repetition is allowed. Note: We can also use the multiplication principle to answer this question.

Now these three numbers can be arranged among themselves in ascending order in only 1 way. Hence total no. of ways = 9C3 × 1 = 84.

Thus, 3-digit numbers can be formed in 60 ways without repetition. Q. (i) repetition of the digits is allowed? (ii) repetition of the digits is not allowed?

Remaining places can be filled by 2, 3, 6, 7 or 9. There is 5 possible ways to fill ten's place. There is 4 possible ways to fill hundredth place as digits cannot be repeated. ∴ 3 - digit numbers can be formed from the digits 2, 3, 5, 6, 7 and 9 is 20.

What are the possible combinations of 1 2 3 4 5 6? ›

There are 720 permutations of the digits 1,2,3,4,5,6. Suppose these permutations are arranged from smallest to largest numerical values, beginning from 123456 and ending with 654321.

But there are 4 different numbers. So the number of 3-number combinations are- (1,2,3),(1,2,4),(1,3,4),(2,3,4). Each can be arranged in 6 ways, so we get 24 ways totally.

= 4*3*2*1/2*1 = 4*3 = 12. Numbers formed by repetition are 11,22,33,44.

∴ Required number of numbers = (1 x 5 x 4) = 20. How many 3-digit numbers can be formed from the digits 2, 3, 5, 6, 7 and 9, which are divisible by 5 and none of the digits is repeated?

There are 9 ways to pick the 1st digit For each of those 9 ways there are 8 ways to choose the second digit. That's 9 x 8 or 72 ways to pick the first two digits. For each of those 72 ways there are 7 ways to choose the third digit. That's 72 × 7 ways or 504 ways to pick all three digits.

⇒So, the required number of ways in which three-digit numbers can be formed from the given digits is 9×8×7=504.

Thus, 3-digit even number can be formed in 108 ways.

So by the multiplication principle (MP), there are 9*9*8 ways to do this. So there are 648 numbers that are 3 digit numbers and have no repeated digits.

The number of 3 digit odd numbers, that can be formed by using the digits 1,2,3,4,5,6 when the repetition is allowed, is. 60.

∴ Required number of numbers = (1 x 5 x 4) = 20.