How many 3 numbers can be formed from the digits 1 2 3 4 and assuming that I repetition of the digits is allowed II repetition of the digits is not allowed?
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(i) When repetition of digits is allowed: (ii) When repetition of digits is not allowed: NCERT Solutions Class 11 Maths Chapter 7 Exercise 7.1 Question 1 How many 3-digit numbers can be formed from the digits 1, 2, 3, 4 and 5 assuming that (i) repetition of the digits is allowed? (ii) repetition of the digits is not allowed?Summary: (i) Total number of 3 digit numbers formed when repetition is allowed = 125, (ii) Total number of 3 digit numbers formed when repetition is not allowed = 60 Problem 1: How many 3-digit numbers can be formed from the digits 1, 2, 3, 4 and 5 assuming that –(i) repetition of the digits is allowed?Solution:
(ii) repetition of the digits is not allowed?Solution:
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:
Problem 3: How many 4-letter code can be formed using the first 10 letters of the English alphabet if no letter can be repeated?Solution:
Problem 4: How many 5-digit telephone numbers can be constructed using the digits 0 to 9 if each number starts with 67 and no digit appears more than once?Solution:
Problem 5: A coin is tossed 3 times and the outcomes are recorded. How many possible outcomes are there?Solution:
Problem 6: Given 5 flags of different colours, how many different signals can be generated if each signal requires the use of 2 flags, one below the other?Solution:
How many 3Problem 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 3Solution : (i) When repetition of digits is allowed: How many 3I was able to get this question, by changing 2, 3, 4 and 5 to 1, 2, 3 and 4; then multiplying 4 by 3 by 2 to give 24 possibilities. How many 3How many 3-digit numbers can be formed from the digits 1, 2, 3, 4 and 5 assuming that repetition of the digits is not allowed. = m x n x p = 5 x 4 x 3 = 60. How many 3-digit numbers can be formed from the digits 1, 2, 3, 4 and 5 assuming that repetition of the digits is allowed. Number of places for the digits = 3. How many 3Problem 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.
How many numbers of 3 digits can be formed with the digits 1 2 3 4 and 5 without any repetition of digits?∴ Total number of 3-digit numbers = 3×4×5=60.
How many 3Solution : (i) When repetition of digits is allowed:
No. of ways of choosing firsy digits = 5 No. of ways of choosing second digit = 5 No. of ways of choosing third digit = 5 Therefore, total possible numbers `= 5 xx 5 xx 5 = 125` (ii) When repetition of digits is not allowed: No. How many 3How many 3-digit numbers can be formed from the digits 1, 2, 3, 4 and 5 assuming that repetition of the digits is not allowed. = m x n x p = 5 x 4 x 3 = 60. How many 3-digit numbers can be formed from the digits 1, 2, 3, 4 and 5 assuming that repetition of the digits is allowed. Number of places for the digits = 3.
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