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Using the digit from the set Q = (5, 6, 7, 8, 9), no digit being used

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Bunuel
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Using the digit from the set Q = (5, 6, 7, 8, 9), no digit being used [#permalink] New post   04 Jun 2019, 01:09
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A
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94% (00:57) correct 6% (01:30) wrong based on 68 sessions
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Using the digit from the set Q = (5, 6, 7, 8, 9), no digit being used more than once, how many 3-digit numbers smaller than 600 can be made?

A. 10
B. 11
C. 12
D. 13
E. 14
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C
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Re: Using the digit from the set Q = (5, 6, 7, 8, 9), no digit being used [#permalink] New post   04 Jun 2019, 01:22
The hundred's place is fixed (5). So for the tens and units place we have 4*3 possibilities = 12 Option C
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Re: Using the digit from the set Q = (5, 6, 7, 8, 9), no digit being used [#permalink] New post   04 Jun 2019, 03:03
Bunuel wrote:
Using the digit from the set Q = (5, 6, 7, 8, 9), no digit being used more than once, how many 3-digit numbers smaller than 600 can be made?

A. 10
B. 11
C. 12
D. 13
E. 14


hundered = 5; 1
tens= 4
unit 3
1*4*3 ; 12
IMO C
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Re: Using the digit from the set Q = (5, 6, 7, 8, 9), no digit being used [#permalink] New post   06 Jun 2019, 05:24
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_ _ _ 3 digit number

Since number <600,
therefore

1st digit = 5
2nd = 6/7/8/9
3rd = 7/8/9 (or any 3 digits left after the first two blanks filled; since no repetition)

P = 1 * 4 * 3
= 12
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Re: Using the digit from the set Q = (5, 6, 7, 8, 9), no digit being used [#permalink] New post   09 Jun 2019, 19:36
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Bunuel wrote:
Using the digit from the set Q = (5, 6, 7, 8, 9), no digit being used more than once, how many 3-digit numbers smaller than 600 can be made?

A. 10
B. 11
C. 12
D. 13
E. 14


Since the number must be less than 600, the first digit (i.e., the hundreds digit) must be 5. Then we have 4 options for the next (tens) digit and 3 options for the ones digit. Thus, the number can be created in 1 x 4 x 3 = 12 ways.

Answer: C
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gmatclubot
Re: Using the digit from the set Q = (5, 6, 7, 8, 9), no digit being used [#permalink]
09 Jun 2019, 19:36
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