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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How many 3-digit numbers can be formed from the digits 1, 2, 3, 4 and 5 assuming that:1) Repetition is not allowed.2) Repetition is allowed.Answer VerifiedHint: Fundamental principle of counting: According to the fundamental principle of counting if a task can be done in “m” ways and another task can be done in “n” ways, then the number of ways in which both the tasks can be done in mn ways. Complete step by step solution: Note: The number of 3-digit numbers formed using the digits 1, 2, 3, 4 and 5 when repetition is not allowed is equivalent to the number of 3 Letter permutations of 5 distinct letter = ${}^{5}{{P}_{3}}=\dfrac{5!}{\left( 5-3 \right)!}=\dfrac{5!}{2!}=\dfrac{120}{2}=60$ which is the same result as above. 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.
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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