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The total number of 5-digit numbers that can be composed of distinct digits from 0 to 9 is
- a)45360
- b)30240
- c)27216
- d)15120
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
The total number of 5-digit numbers that can be composed of distinct d...
There are 9 choices for the first digit, since 0 can't be used. For the second digit, you can use any of the remaining 9 digits.
For the third digit you can use any of the 8 digits not already used.
For the next digit, there are 7 choices. And for the final digit there are 6 choices left.
Multiplying the values together gives the stated answer: 9 × 9 × 8 × 7 × 6 = 27216
If the last 4 don't include 0, you only have 5 choices left for the first one.
Since the number of distinct-4-digits arrangements which don't include a 0 is 9C4 × 4!
= 9 × 8 × 7 × (30 + 60 − 36)
= 9 × 9 × 8 × 7 × 6 = 27216
For the third digit you can use any of the 8 digits not already used.
For the next digit, there are 7 choices. And for the final digit there are 6 choices left.
Multiplying the values together gives the stated answer: 9 × 9 × 8 × 7 × 6 = 27216
If the last 4 don't include 0, you only have 5 choices left for the first one.
Since the number of distinct-4-digits arrangements which don't include a 0 is 9C4 × 4!
= 9 × 8 × 7 × (30 + 60 − 36)
= 9 × 9 × 8 × 7 × 6 = 27216
Most Upvoted Answer
The total number of 5-digit numbers that can be composed of distinct d...
There are 10 digits available to choose from (0 to 9) and we need to form a 5-digit number using distinct digits.
To solve this problem, we can break it down into steps:
Step 1: Choose the first digit
Since the number cannot start with zero, we have 9 options for the first digit (1 to 9).
Step 2: Choose the second digit
After selecting the first digit, we have 9 remaining digits to choose from for the second position (0 to 9 excluding the digit already chosen for the first position).
Step 3: Choose the third digit
Similarly, after selecting the first two digits, we have 8 remaining digits to choose from for the third position.
Step 4: Choose the fourth digit
After selecting the first three digits, we have 7 remaining digits to choose from for the fourth position.
Step 5: Choose the fifth digit
Finally, after selecting the first four digits, we have 6 remaining digits to choose from for the fifth position.
At each step, the number of options decreases by 1, since we are using distinct digits. Therefore, the total number of 5-digit numbers that can be composed of distinct digits is given by:
9 x 9 x 8 x 7 x 6 = 27216
Hence, the correct answer is option C) 27216.
To solve this problem, we can break it down into steps:
Step 1: Choose the first digit
Since the number cannot start with zero, we have 9 options for the first digit (1 to 9).
Step 2: Choose the second digit
After selecting the first digit, we have 9 remaining digits to choose from for the second position (0 to 9 excluding the digit already chosen for the first position).
Step 3: Choose the third digit
Similarly, after selecting the first two digits, we have 8 remaining digits to choose from for the third position.
Step 4: Choose the fourth digit
After selecting the first three digits, we have 7 remaining digits to choose from for the fourth position.
Step 5: Choose the fifth digit
Finally, after selecting the first four digits, we have 6 remaining digits to choose from for the fifth position.
At each step, the number of options decreases by 1, since we are using distinct digits. Therefore, the total number of 5-digit numbers that can be composed of distinct digits is given by:
9 x 9 x 8 x 7 x 6 = 27216
Hence, the correct answer is option C) 27216.
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The total number of 5-digit numbers that can be composed of distinct digits from 0 to 9 isa)45360b)30240c)27216d)15120Correct answer is option 'C'. Can you explain this answer?
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