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How many positive integers, between 300 and 3,000, can be formed using
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21 Jan 2022, 07:00
21 Jan 2022, 07:00
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How many positive integers, between 300 and 3,000, can be formed using the digits {0, 1, 2, 3, 5, 7, 8} so that the repetition of the digits is not allowed?
A. 180
B. 340
C. 360
D. 450
E. 570
A. 180
B. 340
C. 360
D. 450
E. 570
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Re: How many positive integers, between 300 and 3,000, can be formed using
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21 Jan 2022, 10:02
21 Jan 2022, 10:02
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Carcass wrote:
How many positive integers, between 300 and 3,000, can be formed using the digits {0, 1, 2, 3, 5, 7, 8} so that the repetition of the digits is not allowed?
A. 180
B. 340
C. 360
D. 450
E. 570
A. 180
B. 340
C. 360
D. 450
E. 570
We need to calculate the 3-digit possibilities separately from the 4-digit possibilities.
3-digit numbers
The first digit can be 3, 5, 7 or 8 (4 ways to choose the first digit)
The second digit can be any digit other than the digit chosen for the first digit (so, (6 ways to choose the second digit)
The third digit can be any digit other than first 2 digits chosen (so, (5 ways to choose the third digit)
So, the TOTAL 3-digit numbers = (4)(6)(5) = 120
4-digit numbers
The first digit can be 1 or 2 (2 ways to choose the first digit)
The second digit can be any digit other than the digit chosen for the first digit (so, (6 ways to choose the second digit)
The third digit can be any digit other than first 2 digits chosen (so, (5 ways to choose the third digit)
The fourth digit can be any digit other than first 3 digits chosen (so, (4 ways to choose the fourth digit)
So, the TOTAL 4-digit numbers = (2)(6)(5)(4) = 240
So, the total number of positive integers between 300 and 3,000 that satisfy the given condition = 120 + 240 = 360
gmatclubot
Re: How many positive integers, between 300 and 3,000, can be formed using [#permalink]
21 Jan 2022, 10:02
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