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How many different 6-digit positive integers are there, wher
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21 Apr 2019, 11:17
21 Apr 2019, 11:17
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Question Stats:
46% (03:32) correct
53% (02:37) wrong based on 13 sessions
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How many different 6-digit positive integers are there, where 3 of the digits are each one of the digits 5 or 7, and the other 3 digits are each of one of the digits 1, 4, 6, or 8 ?
A. 5,760
B. 7,290
C. 7,680
D. 8,640
E. 10,240
A. 5,760
B. 7,290
C. 7,680
D. 8,640
E. 10,240
Re: How many different 6-digit positive integers are there, wher
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25 Apr 2019, 10:38
25 Apr 2019, 10:38
Carcass wrote:
How many different 6-digit positive integers are there, where 3 of the digits are each one of the digits 5 or 7, and the other 3 digits are each of one of the digits 1, 4, 6, or 8 ?
A. 5,760
B. 7,290
C. 7,680
D. 8,640
E. 10,240
A. 5,760
B. 7,290
C. 7,680
D. 8,640
E. 10,240
Please provide a detailed answer.
Re: How many different 6-digit positive integers are there, wher
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25 Apr 2019, 14:36
25 Apr 2019, 14:36
1
Expert Reply
This is really hard to figure it out . However, there is always a way to find out.
1) Now, the stem says that we do have a number with six digits I.E 178,560
each of the three digits could be 5 or 7. The first could be 5 or 7, the second 5 or 7, the third 5 or 7.
This way is like to choose 3 objects from six
\(\frac{6!}{3!*3!} = 20\) different ways
2) For each specification of which 3 digits will each be one of the digits 5 or 7, there are 2 possibilities for each of the 3 digits that are each one of the digits 5 or 7. Therefore the number of different ways to specify these 3 digits is 2 x 2 x 2 = 4 x 2 = 8.
There are 20 different ways to specify which 3 digits will each be one of the digits 5 or 7.
For each specification of which 3 digits will each be one of the digits 5 or 7, there are 8 ways to specify each of these 3 digits.
3) For each specification of which 3 digits will each be one of the digits 5 or 7, and for each specification of which digit each of those 3 digits will be, there are 4 possibilities for each of the other 3 digits that are one of the digits 1, 4, 6, or 8. The number of ways to specify each of the 3 digits that are each one of the digits 1, 4, 6, or 8 is 4 x 4 x 4 = 16 x 4 = 64.
Therefore, in the end
the number of possible 6-digit integers that meet all the requirements of the question stem is 20 x 8 x 64 = 10,240.
E is the answer
1) Now, the stem says that we do have a number with six digits I.E 178,560
each of the three digits could be 5 or 7. The first could be 5 or 7, the second 5 or 7, the third 5 or 7.
This way is like to choose 3 objects from six
\(\frac{6!}{3!*3!} = 20\) different ways
2) For each specification of which 3 digits will each be one of the digits 5 or 7, there are 2 possibilities for each of the 3 digits that are each one of the digits 5 or 7. Therefore the number of different ways to specify these 3 digits is 2 x 2 x 2 = 4 x 2 = 8.
There are 20 different ways to specify which 3 digits will each be one of the digits 5 or 7.
For each specification of which 3 digits will each be one of the digits 5 or 7, there are 8 ways to specify each of these 3 digits.
3) For each specification of which 3 digits will each be one of the digits 5 or 7, and for each specification of which digit each of those 3 digits will be, there are 4 possibilities for each of the other 3 digits that are one of the digits 1, 4, 6, or 8. The number of ways to specify each of the 3 digits that are each one of the digits 1, 4, 6, or 8 is 4 x 4 x 4 = 16 x 4 = 64.
Therefore, in the end
the number of possible 6-digit integers that meet all the requirements of the question stem is 20 x 8 x 64 = 10,240.
E is the answer
