How many three digit numbers can be formed by using 0, 1,2,3 and 4 repetition not allowed
The four given digits are 0, 1, 2 and 3. Show
Three-digit numbers are of the form . We need to find the number of 3-digit numbers that can be formed using the given digits without repetition. 0 cannot be at the hundreds place. Thus, the hundreds place can be filled with 3 digits (1, 2 or 3). Then, the tens place can be filled with the remaining 3 digits and the ones place can be filled with the remaining 2 digits. Thus, there are three-digit numbers that can be formed using the given digits without repetition. Complete step-by-step solution: First box will be hundreds, the second box will be tens and the third box will be ones. Now, as the number is 3 – digit, the first box cannot use digit 0, because if we use 0 as first digit, the number will not be a 3 digit number. So, only 4 digits that are 1, 3, 5 and 7 can be used in the first box. Therefore, there are 4 ways to fill the first box. And for the third box too, we can fill it using any of the 5 given digits. Therefore, we get So, therefore the total ways for forming 3 digit number will be Note: Here, note that if repetition were not allowed, then we would have got different answers. For second digit: For third digit: $ \Rightarrow $Total numbers formed when repetition is not allowed$ = 4 \times 4 \times 3 = 48$ How many three-digit numbers can be formed from the digits 0, 1, 3, 5, 6 if repetitions of digits are not allowed? Three-digit number is to be formed from the digits 0, 1, 3, 5, 6 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 three digit number can be formed using the digits 1,2 3 and 4 if repetitions are allowed?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.
How many 3∴ Total number of 3-digit numbers = 3×4×5=60.
How many 3(i) repetition of the digits is allowed? Solution: Answer: 125.
How many 3ANSWER: 120 three-digit numbers can be formed WITHOUT REPETITION OF DIGITS.
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