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# What is the greatest number of four-digit integers whose

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What is the greatest number of four-digit integers whose [#permalink]

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15 Sep 2008, 03:15
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What is the greatest number of four-digit integers whose unit’s digit must be 1, hundred’s digit must be even, if no repetition of digits is allowed?

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15 Sep 2008, 14:03
dancinggeometry wrote:
What is the greatest number of four-digit integers whose unit’s digit must be 1, hundred’s digit must be even, if no repetition of digits is allowed?

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got 7x5x7x1 = 245

I do not know what I am missing?
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15 Sep 2008, 15:19
dancinggeometry wrote:
What is the greatest number of four-digit integers whose unit’s digit must be 1, hundred’s digit must be even, if no repetition of digits is allowed?

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XEX1

= No.of ways if thousands digit is odd + No. Of ways if thousands digit is even
= 4*5*7*1+ 4*4*7*1
= 36*7
=252
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18 Sep 2008, 01:41
x2suresh wrote:
dancinggeometry wrote:
What is the greatest number of four-digit integers whose unit’s digit must be 1, hundred’s digit must be even, if no repetition of digits is allowed?

360
256
252
250
212

XEX1

= No.of ways if thousands digit is odd + No. Of ways if thousands digit is even
= 4*5*7*1+ 4*4*7*1
= 36*7
=252

Nice explanation....good one.
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22 Sep 2011, 18:38
x2suresh wrote:
dancinggeometry wrote:
What is the greatest number of four-digit integers whose unit’s digit must be 1, hundred’s digit must be even, if no repetition of digits is allowed?

360
256
252
250
212

XEX1

= No.of ways if thousands digit is odd + No. Of ways if thousands digit is even
= 4*5*7*1+ 4*4*7*1
= 36*7
=252

x2Suresh,
Can you please elobarate your explanation? I did not understand even a bit of it.
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22 Sep 2011, 23:26
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chawlavinu wrote:
x2suresh wrote:
dancinggeometry wrote:
What is the greatest number of four-digit integers whose unit’s digit must be 1, hundred’s digit must be even, if no repetition of digits is allowed?

360
256
252
250
212

XEX1

= No.of ways if thousands digit is odd + No. Of ways if thousands digit is even
= 4*5*7*1+ 4*4*7*1
= 36*7
=252

x2Suresh,
Can you please elobarate your explanation? I did not understand even a bit of it.

Let me explain,
we are encountering with 2 situations:
1- No. of ways if thousands digit is odd:
---- For thousands digit: 5 potential digits can stand in it: 1 - 3 - 5 - 7 - 9 , but according to the question digit 1 is placed in the "Unit digit". So we have just 4 different alternatives for thousands digit.

---- For hundreds digit: this digit should be even. so we have 5 alternatives: 0 - 2- 4- 6- 8

---- For unit digit: we should put just "1" in this place and nothing else. so we have just 1 option.

---- For tens digit: we can put every digit (but not "1") in this place. but we know that no repetition of digits is allowed. we potentially have 0, 1, ..., 9 options. but "1" is allocated to units digit, and 2 other digits are allocated to hundreds and thousands digits. So we have 7 (10-3=7) options to place in tens digits.

the total possibilities is made by multiplying these alternatives: 4 * 5 * 7 * 1

2- No. of ways if thousands digit is even:
---- For thousands digit: 4 Alternative (we can not use "0" for this place)
---- For hundreds digit: 4 alternatives (basically we have 5 options, but we use one of them in the thousands digit, so we have 4 other options)
---- For unit digit: we have just one option (1)
---- For tens digit: we have 10-3=7 alternatives
the total possibilities: 4 * 4 * 7 * 1

Re: Zumit PS 018   [#permalink] 22 Sep 2011, 23:26
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