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08 May 2023, 07:15
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C
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Difficulty:
95%
(hard)
Question Stats:
33% (02:48) correct
67%
(02:39)
wrong
based on 55
sessions
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There are six cards numbered 0, 0, 1, 2, 3, and 4. How many 3-digit even numbers are possible when picking 3 cards?
A. 30
B. 32
C. 34
D. 36
E. 38
A. 30
B. 32
C. 34
D. 36
E. 38
08 May 2023, 09:41
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There are six cards numbered 0, 0, 1, 2, 3, and 4. How many 3-digit even numbers are possible when picking 3 cards?
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08 May 2023, 09:57
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Bunuel
The three-digit number can either have one zero in it, two zeros in it, or no zeros in it.
Case 1: If the number has no zeros
_ _ _
The units digit can be filled in 2 ways (either 2 or 4)
As we cannot use any zero in this case, we have 3 digits remaining. The tens and hundreds of digits have to be filled using two of these three digits.
The tens and the hundreds digit can be filled in 3 * 2 ways.
Total number of combinations = 2 * 3 * 2 = 12
Case 2: If the number has only one zero
_ _ 0
_ 0 _
There are two sub-cases possible
- Zero appears in the units place
- Zero appears in the tens place
a) Zero appears in the units place
_ _ 0
If zero appears in the units place, the tens and the hundreds place of the number can be filled in 4 * 3 ways.
b) Zero appears in the tens place
_ 0 _
The units place can be filled in 2 ways (either 2 or 4)
The hundreds place of the number can be filled in 3 ways
Sub-Total = 3 * 2
Total = 12 + 6 = 18
Case 3: If the number has two zeros
_ 0 0
If the number has two zeros, one zero should appear in the units place and the other in the tens place.
The hundreds place of the number can be filled in 4 ways.
Total = 4 ways
Net Sum = 12 + 18 + 4 = 34
Option C
