take 2 digit 5 and 7. form them make four digit numbers , using both t...
Two answers are possible.One is with the repetition of digits.The other is without repetition of digits.ANSWER 1: With RepetitionNumbers: 1,2,4,5,7,8There are 4 digits __ __ __ __1st digit can be filled by any of the 6 numbers.Similarly 2nd, 3rd and 4th digits.Hence each digit will have 6 possibilities.Therefore no.of 4 digit numbers that can be formed are 6 x 6 x 6 x 6 = 1296ANSWER 2: Without Repetition4 digits __ __ __ __Now the first digit can be filled by any of the six numbers. Therefore there are 6 possibilitiesThe second digit will have only 5 possibilities as one of the numbers gets used up by the 1st digit.Similarly the 3rd and 4th digits will have 4 and 3 possibilities respectively.Therefore no.of 4 digit numbers that can be formed are 6 x 5 x 4 x 3 = 360
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take 2 digit 5 and 7. form them make four digit numbers , using both t...
Introduction:
To form four-digit numbers using the digits 5 and 7, we need to ensure that both digits are used an equal number of times. This means that each digit should appear twice in the four-digit number. Let's explore how we can achieve this.
Approach 1: Using 5 as the first digit
One possible approach is to use 5 as the first digit in the four-digit number. This means that 5 will appear as the thousands place and the hundreds place. We can then use 7 as the remaining two digits.
To illustrate this approach, let's consider the following steps:
1. Choose 5 as the first digit (thousands place).
2. Choose 5 as the second digit (hundreds place).
3. Choose 7 as the third digit (tens place).
4. Choose 7 as the fourth digit (ones place).
By following these steps, we obtain the four-digit number 5577.
Approach 2: Using 7 as the first digit
Alternatively, we can use 7 as the first digit in the four-digit number. This means that 7 will appear as the thousands place and the hundreds place. We can then use 5 as the remaining two digits.
To illustrate this approach, let's consider the following steps:
1. Choose 7 as the first digit (thousands place).
2. Choose 7 as the second digit (hundreds place).
3. Choose 5 as the third digit (tens place).
4. Choose 5 as the fourth digit (ones place).
Following these steps, we obtain the four-digit number 7755.
Summary:
By following the above approaches, we have formed two four-digit numbers using the digits 5 and 7, ensuring that both digits appear an equal number of times. The numbers are:
1. 5577
2. 7755
Conclusion:
In conclusion, to form four-digit numbers using the digits 5 and 7, we can either use 5 as the first two digits or 7 as the first two digits. By following the provided steps, we obtain the desired four-digit numbers.
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