Question for Abhiram Rao - 6
Probability
Level
2
How many positive integers less than 10000 are there such that they each have only 3 and/or 7 as their digit(s)?
The answer is 30.
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1 solution
From this question, we can understand that we need to calculate 1,2,3,4-digit numbers which has 3 and 7 as their digits because 10000 is the smallest 5 - digit numbers.
1 digit numbers required = 2 (three and seven)
2 digit numbers required = 2 × 2 = 4 (ones digit can be 3 or 7 and tens digit can be 3 or 7)
3 digit numbers required = 2 × 2 × 2 = 8 (ones digit, tens digit, hundreds digit can be 3 or 7)
4 digit numbers required = 2 × 2 × 2 × 2 = 16 (ones digut, tens digit, hundreds digit, thousands digit can be 3 or 7)
So, the answer is 2 + 4 + 8 + 16 = 3 0 .