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- Rohan decided to make collections of numbers greater than 0 and less than a million with the digits 0, 7 and 8.
Question 1:
Rohan decided to make collections of numbers greater than 0 and less than a million with the digits 0, 7 and 8. How many numbers are possible? A. 1086
B. 486
C. 728
Feedback A million is 1000000(first seven digit’s number). So, we need to find how many numbers of less than 7 digits can be formed using the digits 0, 7 and 8.
This can be done as there are 2 possibilities at this first digit ? 7 and 8
At all other places, any of the three numbers can be present. So there are three possibilities for all other digit’s places, therefore possible numbers
Number of 1 digit numbers = 2
Number of 2 digit numbers = 2 × 3 = 6
Number of 3 digit numbers = 2 × 3 × 3 = 18
Number of 4 digit numbers = 2 × 3 × 3 × 3 = 54
Number of 5 digit numbers = 2 × 3 × 3 × 3 × 3 = 162
Number of 6 digit numbers = 2 × 3 × 3 × 3 × 3 × 3 = 486
Total number of such numbers = 2 + 6 + 18 + 54 + 162 + 486 = 728
This can be done as there are 2 possibilities at this first digit ? 7 and 8
At all other places, any of the three numbers can be present. So there are three possibilities for all other digit’s places, therefore possible numbers
Number of 1 digit numbers = 2
Number of 2 digit numbers = 2 × 3 = 6
Number of 3 digit numbers = 2 × 3 × 3 = 18
Number of 4 digit numbers = 2 × 3 × 3 × 3 = 54
Number of 5 digit numbers = 2 × 3 × 3 × 3 × 3 = 162
Number of 6 digit numbers = 2 × 3 × 3 × 3 × 3 × 3 = 486
Total number of such numbers = 2 + 6 + 18 + 54 + 162 + 486 = 728
D. 1000
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