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combinatorics

by Gurpinder » Sat Aug 07, 2010 6:50 am
If the first and last digit must be a 2 or a 4, how many 5-digit numbers are possible?


2*10*10*10*1 = 2000 (which is the wrong answer)

what am i doing wrong?
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by Rahul@gurome » Sat Aug 07, 2010 6:57 am
Gurpinder wrote:If the first and last digit must be a 2 or a 4, how many 5-digit numbers are possible?


2*10*10*10*1 = 2000 (which is the wrong answer)

what am i doing wrong?
1st digit: 2 or 4; 2 ways
5th digit: 2 or 4; 2 ways
2nd digit: 0 to 9; 10 ways
3rd digit: 0 to 9; 10 ways
4th digit; 0 to 9; 10 ways

No. of 5 digit nos. that are possible = 2*2*10*10*10 = 4,000
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by Gurpinder » Sat Aug 07, 2010 7:01 am
Rahul@gurome wrote:
Gurpinder wrote:If the first and last digit must be a 2 or a 4, how many 5-digit numbers are possible?


2*10*10*10*1 = 2000 (which is the wrong answer)

what am i doing wrong?
1st digit: 2 or 4; 2 ways
5th digit: 2 or 4; 2 ways
2nd digit: 0 to 9; 10 ways
3rd digit: 0 to 9; 10 ways
4th digit; 0 to 9; 10 ways

No. of 5 digit nos. that are possible = 2*2*10*10*10 = 4,000
Hey Rahul,

Thanks for the reply. But I have a question. I understand that the 1st digit has 2 options. But then wouldnt the last digit have 1 option left because 1 of those 2 options has already been selected for the 1st digit. so theres only one option left for the last one.?
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- Alfred A. Montapert, Philosopher.
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by Rahul@gurome » Sat Aug 07, 2010 7:25 am
Gurpinder wrote:
Hey Rahul,

Thanks for the reply. But I have a question. I understand that the 1st digit has 2 options. But then wouldnt the last digit have 1 option left because 1 of those 2 options has already been selected for the 1st digit. so theres only one option left for the last one.?
Gurpinder, it is not mentioned in the question that the digits 2 and 4 cannot be repeated, which means repetition of digits is allowed. Does that answer your query?
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by Gurpinder » Sat Aug 07, 2010 7:28 am
Rahul@gurome wrote:
Gurpinder wrote:
Hey Rahul,

Thanks for the reply. But I have a question. I understand that the 1st digit has 2 options. But then wouldnt the last digit have 1 option left because 1 of those 2 options has already been selected for the 1st digit. so theres only one option left for the last one.?
Gurpinder, it is not mentioned in the question that the digits 2 and 4 cannot be repeated, which means repetition of digits is allowed. Does that answer your query?
Ahh... Thank you!
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by Rahul@gurome » Sat Aug 07, 2010 7:32 am
Gurpinder wrote:
Ahh... Thank you!
Welcome!
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