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# How many 6-digit integers greater than 400,000 can be formed such that

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Math Expert
Joined: 02 Sep 2009
Posts: 60605
How many 6-digit integers greater than 400,000 can be formed such that  [#permalink]

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09 Dec 2019, 03:06
1
00:00

Difficulty:

45% (medium)

Question Stats:

77% (01:30) correct 23% (02:06) wrong based on 39 sessions

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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

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Intern
Joined: 23 Oct 2019
Posts: 3
Location: India
Concentration: Marketing, Entrepreneurship
WE: Investment Banking (Insurance)
Re: How many 6-digit integers greater than 400,000 can be formed such that  [#permalink]

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09 Dec 2019, 06:01
Being greater than 400,000 means it must start with 4,5,6 or 7.
So for first digit we have 4 options.
For the second digit we have 5 options, because we can’t repeat the one we used as first digit.
For the third digit we have 4 options.
For the fourth digit we have 3 options.
For the fifth digit we have 2 options.
& For the last digit we have 1 options.

So, we have a total of
4*5*4*3*2*1= 480 OPTION B.
Senior Manager
Joined: 13 Feb 2018
Posts: 494
GMAT 1: 640 Q48 V28
Re: How many 6-digit integers greater than 400,000 can be formed such that  [#permalink]

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09 Dec 2019, 09:00
Lets count the possibilities for each digit
1st digit: 4 numbers (4,5,6,7). We have not counted 2 and 3 as the number must be more than 400 000
2nd digit: 5 numbers (as we have used one number for the first digit)
3rd digit: 4 numbers
4th digit: 3 numbers
5th digit:2 numbers
6th digit: 1 number

So we have got 4*5*4*3*2*1=480

IMO
Ans: B
Re: How many 6-digit integers greater than 400,000 can be formed such that   [#permalink] 09 Dec 2019, 09:00
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