Question 979424: Anna forgot the code of a 3-digit lock on
her case (all digits ranging from 0 to 9).
She remembers that the first digit was
less than 5, the second digit was an odd
number, and the third one was either 7 or
8. There were no identical digits in the
code
How many different combinations could
possibly open her lock?
Answer by anand429(138)   (Show Source):
You can put this solution on YOUR website! Possibilities of 1st digit are 0,1,2,3,4
Possibilities of 2nd digit are 1,3,5,7,9
Possibilities of 3rd digit are 7,8
Now, considering no digits are identical,
For 1st digit 0, 3rd digit-7. 2nd digit options, 1,3,5,9 Total cases=4
For 1st digit 0, 3rd digit-8. 2nd digit options, 1,3,5,7,9 Total cases=5
For 1st digit 1, 3rd digit-7. 2nd digit options, 3,5,9 Total cases=3
For 1st digit 1, 3rd digit-8. 2nd digit options, 3,5,7,9 Total cases=4
For 1st digit 2, 3rd digit-7. 2nd digit options, 1,3,5,9 Total cases=4
For 1st digit 2, 3rd digit-8. 2nd digit options, 1,3,5,7,9 Total cases=5
For 1st digit 3, 3rd digit-7. 2nd digit options, 1,5,9 Total cases=3
For 1st digit 3, 3rd digit-8. 2nd digit options, 1,5,7,9 Total cases=4
For 1st digit 4, 3rd digit-7. 2nd digit options, 1,3,5,9 Total cases=4
For 1st digit 4, 3rd digit-8. 2nd digit options, 1,3,5,7,9 Total cases=5
Total no. of cases = 41
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