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How many 3-digit numbers can be formed without using the digits 0, 2, 3, 4, 5 and 6 ?

  • 120
  • 72
  • 64
  • 36
  • None of these
  • Nội dung chính

    • How many 3-digit numbers can be formed without using the digits 0, 2, 3, 4, 5 and 6 ?
    • Answer (Detailed Solution Below)
    • RD Sharma Solutions Class 6 Mathematics Solutions for Knowing your numbers Exercise 1.1 in Chapter 1 – Knowing your numbers
    • Total number of digits = 5 We cannot have 0 the hundred’s place so, the hundred’s place can be digits with any of the 4 digits 1,3,5 or 7, So, there are 4 ways of filling the hundred’s place can be digits with any of the 4 digits 1,3,5 or 7, So, there are 4 ways of filling the hundred’s palce. Since, the digit may be repeated in three digits numbers. ∴ Ten’s place can be filled with any of the 5 digits in 5 ways And unit’s place can be filled with any of the 5 digits in 5 ways Hence, the
      total number of required numbers = 4×5×5=100
    • How many 3 digits numbers can be formed by using the digits 3 4 5 6 when each digits may be repeated any number of times?
    • How many 3 digit even numbers can be formed from the digits 0 1 2 3 4 and 5 when none of the digits are repeated?
    • How many 3 digit numbers can be formed from the digits 1 2 3 if repetition is allowed?
    • How many 3 digit odd numbers
      can be formed using the digits 0 1 2 3 4 and 5 if I repetition of digits is allowed II repetition of digits is not allowed?
    • How many 3 digit numbers can be formed using the digits 5 7 8 without repeating any of the digits?
    • How many 3 digit numbers will be formed using the digits 0 5 6 7 only once?
    • How many different 3 digit numbers can be formed by using the digit 0 to 5 without repeating any digit in the number?
    • How many 3 digit numbers can be formed without repeating?

    Answer (Detailed Solution Below)

    Option 3 : 64

    Concept:

    Fundamental Principle
    of Multiplication:

    Let us suppose there are two tasks A and B such that the task A can be done in m different ways following which the second task B can be done in n different ways. Then the number of ways to complete the task A and B in succession respectively is given by: m × n ways.

    Fundamental Principle of Addition:

    Let us suppose there are two tasks A and B such that the task A can be done in m different ways and task B can be
    completed in n ways. Then the number of ways to complete either of the two tasks is given by: (m + n) ways.

    Calculation:

    Here, we have to find how many 3-digit numbers can be formed without using the digits 0, 2, 3, 4, 5 and 6.

    i.e we have to find how many 3-digit numbers can be formed using the digits 1, 7, 8, 9.

    Clearly, repetition of digits is allowed.

    The number of ways to fill unit’s digit = 4

    The number of ways
    to fill ten’s digit = 4

    The number of ways to fill hundred’s digit = 4

    ∴ Total number of required numbers = 4 × 4 × 4 = 64

    Stay updated with the Mathematics questions & answers with Testbook. Know more about Permutations and Combinations and ace the concept of Fundamental Principles of Counting.

    RD Sharma Solutions Class 6 Mathematics Solutions for Knowing your numbers Exercise 1.1 in Chapter 1 – Knowing your numbers

    Question 8 Knowing your numbers Exercise 1.1

    Nội dung chính

    • RD Sharma Solutions Class 6 Mathematics Solutions for Knowing your numbers Exercise 1.1 in Chapter 1 – Knowing your numbers
    • Total
      number of digits = 5 We cannot have 0 the hundred’s place so, the hundred’s place can be digits with any of the 4 digits 1,3,5 or 7, So, there are 4 ways of filling the hundred’s place can be digits with any of the 4 digits 1,3,5 or 7, So, there are 4 ways of filling the hundred’s palce. Since, the digit may be repeated in three digits numbers. ∴ Ten’s place can be filled with any of the 5 digits in 5 ways And unit’s place can be filled with any of the 5 digits in 5 ways Hence, the total
      number of required numbers = 4×5×5=100
    • How many 3 digits numbers can be formed by using the digits 3 4 5 6 when each digits may be repeated any number of times?
    • How many 3 digit even numbers can be formed from the digits 0 1 2 3 4 and 5 when none of the digits are repeated?
    • How many 3 digit numbers can be formed from the digits 1 2 3 if repetition is allowed?
    • How many 3 digit odd numbers can be formed using the digits 0 1 2 3 4 and 5 if I repetition of digits is allowed II repetition of digits is not allowed?

    How
    many different 3-digit numbers can be formed by using the digits 0, 2, 5 without repeating any digit in the number?

    Answer:

    The different 3-digit numbers which can be formed by using the digits 0, 2, 5 without repeating any digit in the number are 205, 250, 502 and 520.

    Therefore, four 3 digit numbers can be formed by using the digits 0, 2, 5.

    Was This helpful?

    Solution

    Total number of digits = 5 We cannot have 0 the hundred’s place so, the hundred’s place can be digits with any of the 4 digits 1,3,5 or 7, So, there are 4 ways of filling the hundred’s place can be digits with any of the 4 digits 1,3,5 or 7, So, there are 4 ways of filling the hundred’s palce. Since, the digit may be repeated in three digits numbers. ∴ Ten’s place can be filled with any of the 5 digits in 5 ways And unit’s place can be filled with any of the 5 digits in 5 ways Hence, the
    total number of required numbers = 4×5×5=100

    How many 3-digit numbers can be formed by using the digits 0, 1, 3, 5, 7 while each digit may be repeated any number of times?

    How many 3-digit numbers can be formed by using the digits 0, 1, 3, 5, 7 while each digit may be repeated any number of times?

    How many natural numbers
    greater than 4000 are formed from the numbers 0,1,3,7,9 with the figures not repeated, B) How many will the number of natural numbers be less than 4000, and can the numbers be repeated?

    Your answer:

    Did you find an error or inaccuracy? Feel không lấy phí to write us. Thank you!

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      numbers How many are all three-digit numbers that are made up of digits 0,2,5,7 and are divisible by nine if the digits can be repeated?
    • Repeated 38103 How many 5-digit numbers can we assemble from the number 2,3,4,5,6,7,8,9 if the digit in each number can be repeated only once?
    • Three-digit number How many three-digit natural numbers can we form from the digits 0, 1, and 2 if the numerals can be repeated in these numbers?
    • Natural
      numbers How many natural numbers less than 301 can be created from the numbers 0,1,2,3,6,7?
    • Three-digit How many three-digit natural numbers are greater than 321 if no digit in number repeated?
    • How many 2 How many three-lettered words can be formed from letters A B C D E G H if repeats are: a) not allowed b) allowed.
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      in the number cannot be repeated?
    • 5 digits You have the following digits: 9, 8, 0, 1, 5. Write the smallest even five-digit number if one digit is repeated three times and the other digits are not repeated. The digit sum of the number is: a) 9 b) 6 c) 8 d) 23
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    Text Solution

    Solution : The hundred’s place cannot contain 0. So, it can be filled by any of the digits 1,3,5,7.
    So, there are 4 ways to fill it.
    Now, each of the ten’s and unit’s digits can be filled by any of the given five digits.
    So, each can be filled in 5 ways.
    `therefore` the required number of
    numbers `=(4xx5xx5)=100.`

    How many 3 digits numbers can be formed by using the digits 3 4 5 6 when each digits may be repeated any number of times?

    Problem 2: How many 3-digit even numbers can be formed from the digits 1, 2, 3, 4, 5, 6 if the digits can be repeated? Solution: Answer: 108. Let 3-digit number be XYZ.

    How many 3 digit even numbers can be formed from the digits 0 1 2 3 4 and 5 when none of the digits are repeated?

    Count the number of 3-digit strings whose last digit is even. This gives 60−8=52 3-digit even numbers using digits from 0,1,2,3,4,5 without repetition. Show activity on this post.

    How many 3 digit numbers can be formed from the digits 1 2 3 if repetition is allowed?

    Answer: 125 As repetition is allowed, So the number of digits available for B and C will also be 5 (each).

    How many 3 digit odd numbers
    can be formed using the digits 0 1 2 3 4 and 5 if I repetition of digits is allowed II repetition of digits is not allowed?

    Hence, the number of 3-digit odd numbers that can be formed =3×6×6=108. Q..

    How many 3 digit numbers can be formed using the digits 5 7 8 without repeating any of the digits?

    Solution : 357, 375, 537, 573, 735, 753.

    How many 3 digit numbers will be formed using the digits 0 5 6 7 only once?

    The possible 3-digit numbers are: 507, 705, 750, 570.

    How many different 3 digit numbers can be formed by using the digit 0 to 5 without repeating any digit in the number?

    Answer: The different 3-digit numbers which can be formed by using the digits 0, 2, 5 without repeating any digit in the number are 205, 250, 502 and 520.

    How many 3 digit numbers can be formed without repeating?

    n will be the number of digits that are not in 0, 2, 3, 4, 5 and 6. Hence 1, 7, 8, 9. The value of r will be 3, as we need a form 3 digit number only. Hence, 24 3-digits numbers can be formed without using the digits 0, 2, 3, 4, 5 and 6.
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