How many arrangements of 3 digits can be formed from the digits 0 through 9? (2024)

FAQs

How many arrangements of 3 digits can be formed from the digits 0 through 9? ›

Summary: In 1000 arrangements 3 digits can be formed from the digits 0 through 9.

Since we are talking about the 3 digit arrangements, not the 3 digit numbers, so we have 10 options 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 for each of the three places in the arrangement. Thus, the required number of arrangements is 1000.

where C(n, k) represents the number of combinations of n items taken k at a time, n! denotes the factorial of n, and k is the number of items taken at a time. Therefore, using the digits 0, 2, 3, 5, 6, 8, and 9, we can form a total of 840 three-digit numbers with no digit repeated in each of them.

Expert-Verified Answer

There are 180 different arrangements of the letters in the word "BETTER". The correct answer between all the choices given is the first choice.

We have to choose any digit from 0 to 9 i.e., there are 10 digits available. Therefore, no. of 3 digit numbers possible= 10P3= 10!/3! =720.

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

The answer is 10C3 = 10*9*8/(3*2*1) = 120 combinations.

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?

P_r = n! / (n-r)! For example: The different ways in which the 3 letters, taken 2 at a time, can be arranged is 3!/(3-2)! = 3!/1!

How many different 5 letter arrangements are there in the word digit? ›

The word DIGIT has 5 letters, but has 2 I's which are indistinguishable. Therefore, it can be arranged in 5!/2! = 120/2 = 60 ways.

Since there are no repeating letters, and there are 5 total letters, there are 5!= 120 ways to arrange them.

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?

If what you want are all possible three digit numbers with no repetition of the digits then you have 10 choices for the first digit, you have 9 choices for the 2nd digit, and you have 8 choices for the 3rd digit giving you 10x9x8 = 720 in all.

Solution: Combinations are selections made by taking some or all of a number of objects, irrespective of their arrangements. We have to find the number of arrangements of 3 digits which can be formed from digits 0 to 9. Therefore, in 1000 arrangements 3 digits can be formed from the digits 0 through 9.

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.