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How many 6-digit integers greater than 400,000 can be formed
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03 Dec 2019, 02:47
03 Dec 2019, 02:47
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How many 6-digit integers greater than 400,000 can be formed such that each of the digits 2, 3, 4, 5, 6 and 7 is used once in each 6-digit integer?
A. 240
B. 480
C. 720
D. 960
E. 1,440
Kudos for the right answer and explanation
A. 240
B. 480
C. 720
D. 960
E. 1,440
Kudos for the right answer and explanation
Re: How many 6-digit integers greater than 400,000 can be formed
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04 Dec 2019, 10:44
04 Dec 2019, 10:44
1
How many 6-digit integers greater than 400,000 can be formed such that each of the digits 2, 3, 4, 5, 6 and 7 is used once in each 6-digit integer?
The question asks for a 6-digit number greater than 400,000.
The numbers that we can be used for the hundred-thousands digit is either 4, 5, 6 or 7. We have 4 choices.
4x?x?x?x?x?
For the ten-thousand digit, we can fit them with any number. Meaning, if we use 4 for the hundred-thousand, we can use the other 5 digits - 2, 3, 5, 6, 7. This also applies if we choose another number, let's say 2. We can then choose from 3, 4, 5, 6, 7. Again 5 digits, meaning 5 choices.
4x5x?x?x?x?
Use the same strategy for filling in the rest of the numbers and your equation looks like so.
4x5x4x3x2x1=?
The answer is 480.
B.
The question asks for a 6-digit number greater than 400,000.
The numbers that we can be used for the hundred-thousands digit is either 4, 5, 6 or 7. We have 4 choices.
4x?x?x?x?x?
For the ten-thousand digit, we can fit them with any number. Meaning, if we use 4 for the hundred-thousand, we can use the other 5 digits - 2, 3, 5, 6, 7. This also applies if we choose another number, let's say 2. We can then choose from 3, 4, 5, 6, 7. Again 5 digits, meaning 5 choices.
4x5x?x?x?x?
Use the same strategy for filling in the rest of the numbers and your equation looks like so.
4x5x4x3x2x1=?
Show: ::
The answer is 480.
B.
Re: How many 6-digit integers greater than 400,000 can be formed
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05 Dec 2019, 02:13
05 Dec 2019, 02:13
1
Lets tackle this in 2 cases.
Case 1: we have to make a 6 digit number and it will be greater than 400,000 if the first digit is among 5,6,7. This implies there are 3 ways to fill the first digit, 5 number are left. 2nd digit can be filled in 5 ways, 3rd digit in 4 ways and so on.
3 ways x 5 ways x 4 ways x 3 ways x 2 ways x 1 way = 360 ways.
Case 2: if the first digit is 4, it is filled in 1 way. The next digits can be filled just like we did in above case where every number will be greater than 400,000.
1 way x 5 ways x 4 ways x 3 ways x 2 ways x 1 way = 120 ways.
Summing them up, we have 480 ways.
Case 1: we have to make a 6 digit number and it will be greater than 400,000 if the first digit is among 5,6,7. This implies there are 3 ways to fill the first digit, 5 number are left. 2nd digit can be filled in 5 ways, 3rd digit in 4 ways and so on.
3 ways x 5 ways x 4 ways x 3 ways x 2 ways x 1 way = 360 ways.
Case 2: if the first digit is 4, it is filled in 1 way. The next digits can be filled just like we did in above case where every number will be greater than 400,000.
1 way x 5 ways x 4 ways x 3 ways x 2 ways x 1 way = 120 ways.
Summing them up, we have 480 ways.
