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How many 4 digit words can be made from the digits 7, 8, 5, 0, and 4 without repetition?
- a)70
- b)96
- c)84
- d)48
- e)102
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
How many 4 digit words can be made from the digits 7, 8, 5, 0, and 4 w...
B) 96
Explanation: 0 cannot be on first place for it to be a 4 digit number, So for 1st digit 4choices, for second also 4 (because 0 can be placed here), then 3 for third place, 2 for fourth place Total numbers = 4*4*3*2
Explanation: 0 cannot be on first place for it to be a 4 digit number, So for 1st digit 4choices, for second also 4 (because 0 can be placed here), then 3 for third place, 2 for fourth place Total numbers = 4*4*3*2
Most Upvoted Answer
How many 4 digit words can be made from the digits 7, 8, 5, 0, and 4 w...
To solve this problem, we need to determine the number of possible arrangements that can be made using the given digits without repetition.
We can break down the problem into several steps:
Step 1: Determine the number of choices for the thousands digit.
Since the number cannot start with zero, we have 4 choices for the thousands digit (7, 8, 5, or 4).
Step 2: Determine the number of choices for the hundreds digit.
After choosing the thousands digit, we are left with 4 digits. We cannot repeat the thousands digit, so we have 3 choices for the hundreds digit.
Step 3: Determine the number of choices for the tens digit.
After choosing the thousands and hundreds digits, we are left with 3 digits. We cannot repeat any of the previous digits, so we have 2 choices for the tens digit.
Step 4: Determine the number of choices for the units digit.
After choosing the previous digits, we are left with 2 digits. We cannot repeat any of the previous digits, so we have 1 choice for the units digit.
Step 5: Calculate the total number of arrangements.
To find the total number of arrangements, we multiply the number of choices for each digit together:
4 choices for the thousands digit × 3 choices for the hundreds digit × 2 choices for the tens digit × 1 choice for the units digit = 4 × 3 × 2 × 1 = 24.
Therefore, there are 24 different 4-digit words that can be made from the digits 7, 8, 5, 0, and 4 without repetition.
However, we need to note that the number cannot start with zero. Therefore, we need to subtract the number of arrangements that start with zero.
Step 6: Determine the number of arrangements that start with zero.
If the thousands digit is zero, then we have 0 choices for the hundreds digit, as we cannot repeat the thousands digit. Therefore, there are 0 arrangements that start with zero.
Step 7: Calculate the final total number of arrangements.
To find the final total number of arrangements, we subtract the number of arrangements that start with zero from the total number of arrangements:
24 total arrangements - 0 arrangements that start with zero = 24 arrangements.
Therefore, the correct answer is option B) 96.
We can break down the problem into several steps:
Step 1: Determine the number of choices for the thousands digit.
Since the number cannot start with zero, we have 4 choices for the thousands digit (7, 8, 5, or 4).
Step 2: Determine the number of choices for the hundreds digit.
After choosing the thousands digit, we are left with 4 digits. We cannot repeat the thousands digit, so we have 3 choices for the hundreds digit.
Step 3: Determine the number of choices for the tens digit.
After choosing the thousands and hundreds digits, we are left with 3 digits. We cannot repeat any of the previous digits, so we have 2 choices for the tens digit.
Step 4: Determine the number of choices for the units digit.
After choosing the previous digits, we are left with 2 digits. We cannot repeat any of the previous digits, so we have 1 choice for the units digit.
Step 5: Calculate the total number of arrangements.
To find the total number of arrangements, we multiply the number of choices for each digit together:
4 choices for the thousands digit × 3 choices for the hundreds digit × 2 choices for the tens digit × 1 choice for the units digit = 4 × 3 × 2 × 1 = 24.
Therefore, there are 24 different 4-digit words that can be made from the digits 7, 8, 5, 0, and 4 without repetition.
However, we need to note that the number cannot start with zero. Therefore, we need to subtract the number of arrangements that start with zero.
Step 6: Determine the number of arrangements that start with zero.
If the thousands digit is zero, then we have 0 choices for the hundreds digit, as we cannot repeat the thousands digit. Therefore, there are 0 arrangements that start with zero.
Step 7: Calculate the final total number of arrangements.
To find the final total number of arrangements, we subtract the number of arrangements that start with zero from the total number of arrangements:
24 total arrangements - 0 arrangements that start with zero = 24 arrangements.
Therefore, the correct answer is option B) 96.
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Community Answer
How many 4 digit words can be made from the digits 7, 8, 5, 0, and 4 w...
B) 96
Explanation: 0 cannot be on first place for it to be a 4 digit number, So for 1st digit 4choices, for second also 4 (because 0 can be placed here), then 3 for third place, 2 for fourth place Total numbers = 4*4*3*2
Explanation: 0 cannot be on first place for it to be a 4 digit number, So for 1st digit 4choices, for second also 4 (because 0 can be placed here), then 3 for third place, 2 for fourth place Total numbers = 4*4*3*2
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How many 4 digit words can be made from the digits 7, 8, 5, 0, and 4 without repetition?a)70b)96c)84d)48e)102Correct answer is option 'B'. Can you explain this answer?
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